Unwarping - Wellcome Trust Centre for Neuroimaging_ UCL

							Unwarping
Assumptions of statistical tests in functional imaging


  In order to assign an observed response to a particular brain
structure, or cortical area, the data must conform to a known
anatomical space.

  In order to combine data from different scans from the same
subject, or data from different subjects it is necessary that they
conform to the same anatomical frame of reference.

  Voxel-based analyses assume that the data from a particular
voxel all derive from the same part of the brain. Violations of this
assumption will introduce artifactual changes in the voxel values
that may obscure changes, or differences, of interest. E.g. if
movement of the subject in the scanner pushes a voxel from an
area of low to high signal, this may register as a false-positive
„activation‟.
Pre-processing steps to cope with violations of
             these assumptions

All scans must conform to the same anatomical frame of reference:
Realign the data to 'undo' the effects of subject movement
during the scanning session.




 Data must conform to a known anatomical space: After
realignment the data are then transformed using linear or
nonlinear warps into a standard anatomical space.

Finally, the data are usually spatially smoothed before entering the
analysis proper.
Pre-processing steps to cope with violations of
             these assumptions

All scans must conform to the same anatomical frame of reference:
Realign the data to 'undo' the effects of subject movement
during the scanning session.

!UNWARP!

 Data must conform to a known anatomical space: After
realignment the data are then transformed using linear or
nonlinear warps into a standard anatomical space.

Finally, the data are usually spatially smoothed before entering the
analysis proper.
                Errors after realignment

After realignment, there can be residual errors in images for a
number of reasons.

The residual variance can be dealt with by assuming that it is related
to subject movement.

One way is to account for subject movement in the design matrix of
the analysis proper, by including the movement parameters
estimated from re-alignment as covariates.
Covarying for movement-related errors after
               realignment
  However, this may remove activations of interest if they are
  correlated with movement


        No correction                  Correction by covariation




       tmax=13.38                            tmax=5.06
               Problems with covariation
   Covariation using movement parameters assumes only rigid
   deformation of the image between scans.
   BUT: images are sampled according to gradients of the magnetic
   field B, in 3 image dimensions.
                   ω = γB
ω = resonant frequency B = magnetic field strength
   By applying a gradient field across B0, B varies according to
   position. There will only be one position at which 1H spins are
   precessing at a particular resonant frequency, so can assign
   resultant signal to this location.
   Signals are assigned in 3 image dimensions by applying field
   gradients across B0 in 3 dimensions.
              y     z                                   B0+Gzz
B0              B0                             B0
   B0-Gxx             x B0+Gxx
                                         B0-Gzz
                     Non-rigid deformation
     Knowing the location at which 1H spins will precess at a particular
     frequency and thus where the signal comes from is dependent upon
     correctly assigning a particular field strength to a particular location.

     If the field B0 is homogeneous, then the image is sampled according
     to a regular grid and voxels can be localised to the same bit of brain
     tissue over subsequent scans by realigning, this is because the
     same transformation is applied to all voxels between each scan.

     If there are inhomogeneities in B0, then different deformations will
     occur at different points in the field over different scans, giving rise
     to non-rigid deformation.


B0                                   Expect field strength to be B0
                                     here, so H atoms with signal associated
                                     with resonant frequency ω0 to be located
                                     here.
                                     In fact, because of inhomogeneity, they are
                                     here.
                 Field inhomogeneities
   Due to microscopic gradients or variations in magnetic field
   strengths that occur at interfaces of substances of different magnetic
   susceptibility. E.g., metallic material (ferromagnetic) and the human
   body (diamagnetic).
   Also occurs close to tissue-air and tissue-bone interfaces such as
   around frontal sinuses.
   Field inhomogeneities have the effect that locations on the image
   are „deflected‟ with respect to the real object.

   A deformation field indicates the
directions and magnitudes of location
deflections throughout the FOV with
respect to the real object.




igl.stanford.edu/~torsten/ct-dsa.html
Movement-by-inhomogeneity interactions

 Field inhomogeneities change with the position of the object in the
field, so there can be non-rigid, as well as rigid distortion over
subsequent scans.

The movement-by-inhomogeneity interaction can be observed by
changes in the deformation field over subsequent scans.




The amount of distortion is proportional to the absolute value of the field
inhomogeneity and the data acquisition time. EPI is particularly sensitive
to the effects of magnetic field inhomogeneities because it has long TR
Controlling for movement-by-inhomogeneity
                 interactions

 One solution is to explicitly measure field inhomogeneity by use
 of a field-map (available in the “FieldMap” SPM toolbox). A field
 map then has to be generated for each scan in the time-series.

 Measurement of field-maps is complicated by noise, and rapid
 loss of signal towards the edges of the object.

 In practice, rather than generating a statistical field map for every
 image in the EPI data set, can compute how the statistical maps
 are warped over subsequent scans and then unwarp the statistical
 map itself in order to make accurate identification of activated
 areas.
 Computing how the images are warped over subsequent scans
 requires knowing how the deformation fields change with
 displacement of the subject, i.e. the derivatives of B with respect
 to displacement of the subject.
              Principles of UNWARP

Given the derivative of the field with respect to subject movement,
and the movement parameters estimated from realignment, can
predict the non-rigid deformation in the scan series.

In practice, we know the non-rigid deformation (in terms of extra
variance after realignment) and the subject movement (movement
parameters) so we can estimate the derivatives of the field B 0 with
respect to subject movement – thus estimate how the field is
warped over the time series and „undo‟ this using UNWARP.
     Movements modelled in UNWARP
Translations and rotations in plane perpendicular to B0 will not affect
B0, so only need to model derivatives of B0 with respect to rotations
out of perpendicular plane, i.e. pitching and rolling , .
         x


                                       B0
                     y
             
                        z




In UNWARP there is a (default) option to re-estimate the movement
parameters with each unwarp iteration. This is recommended by
John Ashburner. It is computed via a series of iterations; 1. estimate
movement parameters (, ), 2. estimate deformation fields,  B0,
3. re-estimate movement with new model of magnetic field B0
                  Modelling changes in B0

   The field B0, which changes as a function of displacement , ,
   can be modelled by the first two terms of a Taylor expansion

         B0(, ) = B0 (, ) + [(δB0/ δ)  + (δB0/ δ ) ]




The „static‟ deformation field,       Changes in the deformation field with
Which is the same throughout          subject movement. Estimated via iteration
The time series.                      Procedure in UNWARP.
Calculated using „Fieldmap‟ in
SPM
It is possible to model the next term in the Taylor expansion as well, i.e. the
     second derivative of B with respect to , , but this is not necessary.
Applying the deformation field to the image

   Once the deformation field has been
modelled over time, the time-variant
field is applied to the image.
 effect of sampling a regular object over a
curved surface.

 The image is therefore re-sampled
assuming voxels, corresponding to
the same bits of brain tissue, occur
at different locations over time.
Advantages of incorporating this in pre-
             processing
 One could include the movement parameters as confounds in the
 statistical model of activations.
 However, this may remove activations of interest if they are
 correlated with the movement.

No correction      Correction by covariation   Correction by Unwarp




tmax=13.38               tmax=5.06                tmax=9.57
          UNWARP: Benefits and Limitations
   Although for small movements a limited portion of the total variance
   is removed, the susceptibility-by-movement interaction effects are
   quite localised to "problem" areas. For a subset of voxels in e.g.
   frontal-medial and orbitofrontal cortices and parts of the temporal
   lobes the reduction can be quite dramatic (>90%).

   However, UNWARP only tackles one source of variance after re-
   alignment, and other errors may arise from:

- Susceptibility-dropout-by-movement interaction: Field inhomogeneities can also cause
   signal loss due to through-plane dephasing (which will not be rephased by encoding
   gradients that are all in-plane).


- Spin-history effects: The signal will depend on how much longitudinal magnetisation
   has recovered (through T1 relaxation) since it was last excited (short TR→low signal).
   If the subject moves in the direction of increasing slice number between one
   excitation and the next, then the effective TR will be longer (resulting in increasing
   signal intensity).

- Slice-to-vol effects: The rigid-body model that is used by most motion-correction (e.g.
    SPM) methods assume that any movement will occur between scans. However there
    is also movement within scans – leading to further apparent shape changes.
                         Summary
Movement-by-inhomogeneity interactions can be accommodated during
realignment using “unwarp” in SPM5




WARNING!! UNWARP can be computationally intensive, and therefore take
a long time!
                        References

Jezzard, P. and Clare, S. 1999. Sources of distortion in functional MRI
   data. Human Brain Mapping, 8:80-85
Andersson JLR, Hutton C, Ashburner J, Turner R, Friston K (2001)
   Modelling geometric deformations in EPI time series. Neuroimage
   13: 903-919
John Ashburner‟s slides http://www.fil.ion.ucl.ac.uk/spm/course/#slides
Paul Tofts‟ MRI Physics Course at the IoN (slides not yet on the web –
   TBA)