# SpatPre2 by liaoxiuli4

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```									Spatial Preprocessing II

Karolinska MR-Centre, Stockholm,
Sweden
Outline
• Spatial Normalisation
– Why?
– How?
• Distortion Correction
– Why?
– How?
• Movement-by-susceptibility interaction
– What is?
– How?
Movement Correction: How?
How to make a new image when we know the movement

blank sheet

Transform
co-ordinate
x
For each voxel-centre               
Find co-ordinate
co-ordinate                                       in original image
x=10mm
y=0
=10º
Movement Correction: How?
How do we know the movement?
f1            f2
Let’s say we                                        And we want to find the
have two                                            difference in position
images: f1 and f2                                   between them

f1                       f1                   f1
f2-f1                    x                        y                    

x                    +y                       +

“The way the              “The way the           “The way the
Observed            difference image          difference image       difference image
difference          would have looked         would have looked      would have looked
1mm x-translation”        1mm y-translation”     1 degree rotation”
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]?
Spatial Normalisation: How?
What is a “displacement-map”?
Go to original image
For each voxel-centre                                and find intensity at
in blank sheet.                                  “warped” co-ordinate

Get position in
original space by
displacement.

 x '   x   d x ( x, y ) 
 y '    y    d ( x, y ) 
     y                    
Spatial Normalisation: How?
Example: Rectangle->Ellipse
Go to original image
For every voxel
and find intensity at
position in blank                            warped co-ordinate
sheet

Get position in
original space by
displacement

Template
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
Spatial Normalisation: How?
Component displacement-maps.

y-displacement,
black: downward
translation
white: upward
translation
grey: no translation

x-displacement,
black: leftward
translation
white: rightward
translation
y-displacement   gray: no translation

x-displacement
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
Spatial Normalisation: How?
Remember the square->ellipse map?
square->ellipse map

Each basis-warp multiplied by a weight

+   +    +    +     +   +    +    +

+   +    +    +     +   +    +    +

+   +    +    +     +   +    +    +
x-component of
+   +    +    +     +   +    +    +       square->ellipse map

+   +    +    +     +   +    +    +

+   +    +    +     +   +    +    +

+   +    +    +     +   +    +    +

+   +    +    +     +   +    +        =
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”.
f1         f1         f1
f2-f1         x          y          

x         +y         +

• But what are the “causes” in this case??
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
Me    Not me
Lets try and explain the difference
between “me” and “someone else”
by this y-component basis-warp.

y            f  y                f  

                                 
Not me - Me    y-displacement   Intensity change per   Intensity change
per           y-displacement            per 
Spatial Normalisation: How?
And with more basis functions

f2-f1         y  1 f  y            y   2 f  y
 1                        +2                     +...

f                        f
Unravel                             1                      2

Ditto
 1 
 f1   f1        
f2  f1                      2   e  Aβ  e          Ring a bell?
 1    2        
 
Spatial Normalisation: How?
Remember, that was only the y-components.

f2-f1         y  1 f  y             y   2 f  y
 1                       +2                      +...

f                          f
 1                        2
And the x-
components
x   65 f  x            x   66 f  x
But that
...+65                      +66                       +...    doesn’t really
change the
maths.
f                          f
 65                        66
Distortion Correction: Why?
Distortion Correction: How?
We can measure the field at each point.
GE or GE-EPI                                  Post-processing

Short TE     Long TE

Re Im        Re Im

3D watershed           Inversion into
s           l                      based                    undistorted
phase-                    space (EPI
Phase wrap      unwrapping                     only)
1                 (because -<<)
Weighted least-
square fit of
spatial basis-
functions
Phase evolution during TE
EPI images are
distorted

Distorted image   Field-map tells us how each
voxel should be moved

Corrected image

Correction
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 #
BUT!
• This is known as “residual movement-related
variance”.

“Large” Activation

Intensity in voxel

Scan #
More BUT!
x-, y- and z-   x-, y- and z-
translation      rotation
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
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.
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?)
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             Original           Realigned
vary with subject
orientation.
• Hence, the shape
of the subject will
appear to vary
when imaged at
different positions.
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?
Displacement
Slope goes to derivative field

Pitch () Intercepts
goes to
“constant”
field
Displacement

“Taylor expansion”
Pitch ()
So, how does it affect the data?
f1         f2           B0        f1 y

-           2•            
2= 4.7°
...

...
f1         fi           B0        f1 y

-           i•                        i= -4.1°
But we don’t know the field, right?
f1         f2          B0 1   f1 y        B0 2   f1 y             B0 5   f1 y

-           12•                    +22•                   +...+52•                    +...
f 2                      f 2                           f 2
 1                       2                            5

...

...
...
...

f1         fi          B0 1   f1 y        B0 2   f1 y             B0 5   f1 y

-           1i•                    +2i•                   +...+5i•                    +...
f i                      f i                           f i
 1                       3                            5

 1  
A   
f1  f2  f2 1 f 2  2         f2 5                 2 
                                                      2    

Or                  
 f1  fi   fi 1 fi  2        fi  5
  
   
   β  Aβ
          
A   
  5   i 
                                                   
    
        
Validation against measured field maps.
• Dual echo-time EPI data collected at each time-point.
• Phase-maps estimated using “standard” techniques.
Time series
TE=30ms      TE=40ms                  TE=30ms      TE=40ms

Re Im        Re Im                   Re Im         Re Im
1st   TR                          2nd TR     ...

s           l                      s             l

2
1

Weighted least-        Inversion
square fit of          into
3D watershed based              spatial basis-         undistorted
phase-unwrapping                functions              space
Are the field-maps properly explained
by a 1st order Taylor expansion?
1st
Measured
field maps
40th
Taylor
says
         +            +            + error

B0{i}       B0         B0          B0 
Thus
predicting
these

With this
error
Comparing estimated and measured
derivative fields.
• Derivative field with respect to
pitch estimated directly from
time series and from field-maps.
Estimated                     Measured
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
Derivative-fields from different subjects
Subject #1      Subject #2

Derivative
with respect
to pitch

Derivative
with respect
to roll
More Movies
Realigned           Realigned & Unwarped
A (slightly contrived) example:

tmax=9.80
Regression        Unwarp

tmax=8.03        tmax=9.76
A (slightly contrived) example:

tmax=13.38
Regression                    Unwarp

tmax=5.06                    tmax=9.57
Spin-history or
“must remember to move”?
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.

```
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