Spatial Preprocessing II

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Spatial Preprocessing II

• Jesper L.R. Andersson
• Karolinska MR-Centre, Stockholm, Sweden

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Outline

• Spatial Normalisation
• Why?
• How?
• Distortion Correction
• Why?
• How?
• Movement-by-susceptibility interaction
• What is?
• How?

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Movement Correction How?How to make a new image
when we know the movement
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Movement Correction How?How do we know the
movement?
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Spatial Normalisation Why?

• We want to pool results across subjects
• We want to report results in a concise format

Me
Someone else

• Should we pool activations in the yellow voxel?
  
• Is it meaningful to say I activated voxel 25 60
  20?

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Spatial Normalisation How?What is a
displacement-map?
Get position in original space by adding
pertinent displacement.
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Spatial Normalisation How?Example
Rectangle-gtEllipse
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Spatial Normalisation How?Right, but how do we
get the displacement field?

• First we must find a good way to represent the
  field.

Original image
Warped image
Silly displacement-map
Template
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Spatial Normalisation How?Component
displacement-maps.
y-displacement
x-displacement
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Spatial Normalisation How?Representing the
field with basis-warps.

• To prevent impossible deformations we restrict it
  to be a linear combination of permitted
  basis-warps.
• One can for example use the discrete cosine set

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Spatial Normalisation How?Remember the
square-gtellipse map?
square-gtellipse map
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Spatial Normalisation How?But how do we find
the displacement-map?

• Remember realignment? We assumed that the
  observed difference was a linear combination of
  different causes.
• But what are the causes in this case??

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Spatial Normalisation How?But how do we find
the displacement-map?

• The causes in this case are differences in
  shape. These are represented by the basis-warps

Not me
Me
Lets try and explain the difference between me
and someone else by this y-component basis-warp.
?
?
?
?
?
Not me - Me
y-displacement per ?
Intensity change per y-displacement
Intensity change per ?
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Spatial Normalisation How?And with more basis
functions
f2-f1
Unravel
Ditto
Ring a bell?
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Spatial Normalisation How?Remember, that was
only the y-components.
f2-f1
And the x-components
But that doesnt really change the maths.
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Distortion Correction Why?
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Distortion Correction How?We can measure the
field at each point.
Post-processing
GE or GE-EPI
3D watershed based phase-unwrapping
Inversion into undistorted space (EPI only)
Phase wrap (because -?lt?lt?)
??1
Weighted least-square fit of spatial
basis-functions
Phase evolution during ?TE
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EPI images are distorted
Distorted image
Corrected image
Correction
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Movement Correction Revisited

• Sensitivity Large error variance may prevent us
  from finding activations.
• Specificity Task correlated motion may pose as
  activations.

Large Activation
Intensity in voxel
Scan
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BUT!

• This is known as residual movement-related
  variance.

Large Activation
Intensity in voxel
Scan
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More BUT!
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Now, why on earth is that?

• Movement-by-susceptibility-distortion interaction
• Movement-by-susceptibility-dropout interaction
• Spin-history effects
• Interpolation errors
• Movement during acquisition of volume

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What can we do about it?I The sledgehammer
(regression)

• Include movement parameters as confounds in
  statistical model
• Will remove all variance that correlates with
  movements. Protects against false positives.
• Will remove all variance that correlates with
  movements. May remove activations.

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What can we do about it?II Modelling the effects

• Using physics based models to assess and correct
  for all adverse effects of motion.
• Correct thing to do
• Cannot yet model all effects
• Movement-by-susceptibility-distortion
  interaction. modelled by SPM (Unwarp).
• Movement-by-susceptibility-dropout interaction. ?
• Spin-history effects. Prospective motion
  correction?
• Interpolation errors. Not a problem!?
• Movement during acquisition of volume. Modelled
  by Peter Bannister and Mark Jenkinson (FSL?)

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Movement-by-susceptibility-distortion interaction

• The subject will disrupt the B0 field, rendering
  it inhomogeneous.
• This will cause spatial distortions in EPI images.

• The distortions vary with subject orientation.
• Hence, the shape of the subject will appear to
  vary when imaged at different positions.

Realigned
Original
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Describing the field

• In principle there is a unique ?B0 field for each
  subject position. How can we describe the problem
  to make it mathematically tractable?

Slope goes to derivative field
Intercepts goes to constant field
Taylor expansion
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So, how does it affect the data?
?2 4.7
?i -4.1
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But we dont know the field, right?
...
...
...
...
Or
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Validation against measured field maps.

• Dual echo-time EPI data collected at each
  time-point.
• Phase-maps estimated using standard techniques.

Time series
...
??2
??1
Weighted least-square fit of spatial
basis-functions
Inversion into undistorted space
3D watershed based phase-unwrapping
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Are the field-maps properly explained by a 1st
order Taylor expansion?
1st
Measured field maps
40th
Taylor says
?
??
??
error
Thus predicting these
With this error
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Comparing estimated and measured derivative
fields.

• Derivative field with respect to pitch estimated
  directly from time series and from field-maps.

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Derivative-fields estimated from different
time-series

• Derivative field with respect to pitch estimated
  from two different time series on the same subject

Small movements ?2º
Large movements ?6º
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Derivative-fields from different subjects
Derivative with respect to pitch
Derivative with respect to roll
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More Movies
Realigned
Realigned Unwarped
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A (slightly contrived) example Movement and task
uncorrelated
tmax9.80
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Movement and task uncorrelated
Regression
Unwarp
tmax8.03
tmax9.76
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A (slightly contrived) example Movement and task
correlated
tmax13.38
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Movement and task correlated
Regression
Unwarp
Spin-history or must remember to move?
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Conclusion

• Subjects move! There will be movement-related
  variance in the data.
• If movement uncorrelated with task.
• Slight loss of sensitivity. Regression, Unwarp or
  ignoring it all fine.
• If movement correlated with task.
• Loss of specificity. Must be remedied.
• Regression always restores specificity, but may
  cause large loss of sensitivity.
• Unwarp partially restores specificity. Causes no
  loss of sensitivity.