Waterloo NMR Summerschool

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Waterloo NMR Summerschool

• G. Moran
• morang_at_mcmaster.ca
• June 2, 2006

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IMAGE FORM
I Image intensity ? (1 e-TR/T1) e-TE/T2
Images of mystery fruit from Dr. Paul Picot,
formerly LHRI, now GE in London ON
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The Spin-Echo (90-180)

• Wait TR to reach eqm
• Then repeat with new phase
• encodes
• Then repeat for other slices

For a single slice, the total time is TRxNpe ?
1sx256 ? 4.3min
From Principles of MRI, D.G. Nishimura
I Image intensity ? (1 e-TR/T1) e-TE/T2
Note that if TR is long, and TE is shorter, we
get a proton density weighted image
T1-weighting short TE, TR?T1 I ? 1
e-TR/T1
T2-weighting long TR, TE?T2 I ? e-TE/T2
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References

• Principles of MRI, D.G. Nishimura
• http//www.cis.rit.edu/htbooks/nmr
• http//www.cis.rit.edu/htbooks/mri
• Principles of MR, C.P. Slichter, ch 7.28 in 3rd
  Ed
• Principles of NMR Microscopy, P.T. Callaghan

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IMAGE FUNCTION
Normal
Reperfused
Ischemic
Courtesy of Dr. Frank Prato, LHRI, London, ON
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(No Transcript)
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What Makes MRI different from NMR?

• With MRI 3T is considered high field
• 30cm is a small bore MRI
• Very rarely is duct tape ever seen on an MRI unit
  (on the outside at least)
• SPATIAL LOCALIZATION!

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Spatial Localization?

• Consider a cubic volume that has 1mm3 voxels.
• Each voxel has its own magnetization vector
• These vectors are initially aligned with the
  field, B0.

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Question What happens if we 1) Apply a 90
degree pulse?
All of the magnetization vectors are oscillating
at ?0, so all of the vectors are tilted into the
x-y plane (very nearly)
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Question What happens if we 1) Apply a 90
degree pulse?
B0
All of the magnetization vectors are oscillating
at ?0, so all of the vectors are tilted into the
x-y plane (very nearly)
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Slice by Slice Imaging

• We dont want to tilt all the spins
• We want to just excite a slice of spins
• That way we can reduce the 3D problem to a 2D one
• We can do 2D FT NMR
• How can we do this?
• Recall the chemical shift
• Different chemical environments or local fields
  imply that different sites will experience a
  different resonant frequency.
• Lets use a magnetic field gradient to force the
  Larmor frequency to be different at different
  locations

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Science Pays Off?
Taken without permission
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OK. Back to our question 2) We want to image a
single slice through the object. What if we were
to add a small amount to the field so that it
varied with z position?
B(z) B0 Gz z OR ?(z) ?0 ?Gz z
Typically, gradient strengths are 10mT/m
1G/cm whereas B0 1-3T
So, d?/dz ? Gz 4.258 kHz/cm That means that a
physical width of 1cm corresponds to a
frequency width of 4.3kHz.
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Slice Selection

• We can select which physical slice we want by
  choosing the appropriate frequency with our 90
  degree pulse.
• The physical width of the slice, ?z, will be
  determined by the bandwidth of the RF pulse.
• Why a sinc?

BW 2/t ?Gz?z/2p - more lobes in sinc -
better slice profile - longer pulse duration
for same BW
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Slice Selection Summary
So, lets apply a Gz, and a sinc shaped pulse at
?0, with some bandwidth corresponding to ?z.
What happens?
Note that we will only see signal from the
affected spins (only ones in x-y plane). We have
tilted spins in, or excited a single slice.
Now the problem is a 2D one.
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Aside Whats that negative lobe of the
z-gradient for?

• The Bloch equations predict a solution for the
  magnetization in the rotating frame

• The integral leads to the Fourier relationship
  between B1 and Magnetization
• The term in front leads to a dephasing induced
  signal loss.
• Lets take a break and look at it in detail

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Pulse Sequence so far
Now what? We have excited a single slice, now we
need to resolve x and y.
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What if we do nothing?
If we just sit back and wait, we will simply just
detect a FID from all of the spins we have
excited in the slice, as they decay back to
equilibrium.
FID All of the spins in the slice have the same
resonant frequency so all contribute similarly to
the FID. What if we turned on an x gradient, Gx,
while this was happening instead? Well. The
nuclear spins would have a different resonant
frequency depending upon their x position. So
what?
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Turn on a Gx
B(x) B0 Gx x ?(x) ?0 ?Gx x
Think about the received signal from a single
oscillator at x,y Signal
m(x,y) e-i?t The total received signal will be a
sum of all of these in the slice
S ?x?y m(x,y) e-i?t dx dy
?x?y m(x,y) e-i?ot e-i?Gx xt dx dy
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Fourier Transforms
IE) If we receive the signal, then do an inverse
1-D FT, we dont get m(x,y), but a sum of m(x,y)
over y. S ?x ?y m(x,y) dy e-i?Gx xt dx

This makes sense right? The gradient only makes
the resonant frequency a function of x. So when
we look at a single frequency, we see the signal
from one x-position, but all y positions in the
volume.
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Readout Gradient
B(x) B0 Gx x ?(x) ?0 ?Gx x
S(f)
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Readout Gradient

• The x gradient is called the readout gradient,
  because we apply it while reading the signal
• Only during this time does the resonant frequency
  change with x position
• Pulse sequence so far

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The last piece

• Well, what about y?
• Can we apply a Gy during readout too?
• No? Why not?
• The resonant frequency may not be unique across
  the sample

• We do apply a Gy,
• but in a different way.

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Pulse Sequence so far

• We apply a Gy as soon as the slice is selected
• But we only apply it for a time, ty.

Whats this for? Wait for it.
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Phase Encoding?
Each spin, or voxel magnetization vector,
acquires a phase, ?ty, during this time, ty.
?ty ?0ty ?Gyyty
Gy is called the phase encoding gradient. Think
about it another way
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What happens from the spins perspective?
Now when we apply an x gradient, we have two
pieces of information. The spins are rotating at
different frequencies depending upon x, and They
start spinning at different phases depending upon
y.
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The 2DFT Approach

• In this Scheme, the y-gradient introduces a
  phase offset
• Whereas during readout, the x-gradient makes the
  x-direction
• linearly related to frequency
• Mathematically they contribute similar terms to
  the signal

Position (x,y) and Frequency (kx,ky) are Fourier
pairs! So how we sample this k-space has
implications for our image.
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Lets put it all together

• Assume slice is selected
• For each phase encode, an echo is digitized while
  the readout gradient is applied
• For example 256 Echoes might be collected

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Fourier Space
Is related to
From Principles of MRI, D.G. Nishimura
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Lets put it all together

• The position in k-space is dictated by the
  application of the x and y gradients.
• The readout gradient is applied while recording
  the echo
• This causes kx(t) ?/2p Gx t to
  increase

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K-Space?
This is a very useful tool to understand how
various pulse sequences are designed to optimize
the acquisition of frequency space.
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More Advanced Sequences?
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More Advanced Sequences?
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Implications of Sampling k-space

• FOV
• Resolution
• Aliasing
• Etc
• Use 770 notes