Dear everyone,

this mail contains some information regarding a new toolbox that is now
available for download from the FIL website. You will be able to work
your way from the SPM99 page of the FIL home page to find it.

All the usual disclaimers apply, and perhaps yet some since I am not as
experienced a Matlab programmer as e.g. John and Karl.

It is called "Unwarp", and is concerned with the issue of residual
movement related variance in fMRI data.

Even after realignment there is considerable variance in fMRI time
series that covary with, and is most probably caused by, subject
movements. It is also the case that this variance is typically large
compared to experimentally induced variance. Anyone interested can
include the estimated movement parameters as covariates in the design
matrix, and take a look at an F-contrast encompassing those columns. It
can be quite dramatic. The result is loss of sensitivity, and if
movements are correlated to task specificity. I.e. we may mistake
movement induced variance for true activations. Since this variance is
often large compared to "true activations" even quite moderate
correlations between condition and movement may potentially cause false
positives.

The problem is well known, and several solutions have been suggested. A
quite pragmatic (and conservative) solution is to include the estimated
movement paramters (and possibly squared) as covariates in the design
matrix. Since we typically have loads of degrees of freedom in fMRI we
can usually afford this. The problems occurr when movements are
correlated with the task, since the strategy above will discard "good"
and "bad" variance alike.

The "covariate" strategy described above was predicated on a model were
variance was assumed to be caused by "spin history" effects, but will
work pretty much equally good/bad regardless of what the true underlying
cause is.

Others have assumed that the residual variance is caused mainly by
errors caused by the interpolation kernel in the resampling step of the
realignment. One has tried to solve this through higher order resampling
(huge Sinc kernels, or k-space resampling).

The "adjustment for sampling errors" in SPM is also predicated on the
assumption. The idea there is that the use of a finite size
interpolation kernel (e.g. 9x9x9) will casue sampling errors, but that
it should be possible to calculate a range for how large these errors
can be. Hence let us say a given voxel have the quantity a of variance
correlated with movement, and the calculations show that interpolation
errors may cause at the most the quantity b of variance in this
particular voxel. Then no more than b variance will be removed. This
would potentially allow for the removal of as much variance that can
possibly be explained by movement, while preserving experimentally
induced variance. However, this is true only IF the assumption that
residual movement related variance is caused mainly by interpolation is
true.

The "Unwarp" toolbox is based on a different hypothesis regarding the
residual variance. EPI images are not particularly faithful
reproductions of the object, and in particular there are severe
geometric distortions in regions where there is an air-tissue interface
(e.g. orbitofronal cortex and the anterior medial temporal lobes). In
these areas in particular the observed image is a severly warped version
of reality, much like a funny mirror at a fair ground. When one moves in
front of such a mirror ones image will distort in different ways and
ones head may change from very elongated to seriously flattened. If we
were to take digital snapshots of the reflection at these different
positions it is rather obvious that realignment will not suffice to
bring them into a common space.

The situation is similar with EPI images, and an image collected for a
given subject position will not be identical to that collected at
another. We call this effect suscebtibility-by-movement interaction. The
"Unwarp" toolbox is predicated on the assumption that the
suscebtibility-by-movement interaction is responsible for a sizeable
part of residual movement related variance.

Assume that we know how the deformations change when the subject changes
position (i.e. we know the derivatives of the deformations with respect
to subject position). That means that for a given time series and a
given set of subject movements we should be able to predict the "shape
changes" in the object and the ensuing variance in the time series. It
also means that, in principle, we should be able to formulate the
inverse problem, i.e. given the observed variance (after realignment)
and known (estimated) movements we should be able to estimate how
deformations change with subject movement.

We have made an attempt at formulating such an inverse model, and at
solving for the "derivative fields". A deformation field can be thought
of as little vectors at each position in space showing how that
particular location has been deflected. A "derivative field" is then the
rate of change of those vectors with respect to subject movement. Given
these "derivative fields" we should be able to remove the variance
caused by the suscebtibility-by-movement interaction. Since the
underlying model is so restricted we would also expect experimentally
induced variance to be preserved. Our experiments have also shown this
to be true. Indeed one particular experiment even indicated that in some
cases the method will reintroduce experimental variance that had been
obliterated by movement related variance.

In theory it should be possible to estimate also the "static"
deformation field, yielding an unwarped (to some true geometry) version
of the time series. In practice that doesn't really seem to work. Hence,
the method deals only with residual movement related variance induced by
the suscebtibility-by-movement interaction. I.e. unwarping is to some
"average distortion" of the time series.

The method requires no additional measurements. Given an EPI time-series
and a set of movement parameters (obtained from SPM realign) it will
estimate the derivative fields and remove the associated variance from
the time series. Upon installation the toolbox is reached from the
"Toolboxes" menu, and a additional help page will describe its practical
use.

It should be noted that this is a method intended to correct data
afflicted by a particular problem. If there is little movement in your
data to begin with this method will do you no good. If on the other hand
there is appreciable movement in your data (>1mm or >1deg) it will
remove some of that unwanted variance. If, in addition, movements are
task related it will do so without removing all your "true" activations.

The method attempts to minimise total (across the image volume) variance
in the data set. It should be realised that while (for small movements)
a rather limited portion of the total variance is removed, the
suscebtibility-by-movement interaction effects are quite localised to
"problem" areas. Hence, for a subset of voxels in e.g. frontal-medial
and orbitofronal cortices and parts of the temporal lobes the reduction
can be quite dramatic (>90%).

It should also be noted that the suscebtibility-by-movement interaction
casues differental deformations AND differential signal drop-out. At
present the toolbox deals only with variance caused by the first
component.

So, bottom line: I have this data set with task related movements, if I
used this toolbox can I say that any activations I find is "true" and
not just movement?
It will be "more true" than if you didn't use it, but I would still
recommend quite a bit of caution.

Good Luck
Jesper Andersson
John Ashburner
Chloe Hutton
Bob Turner
Karl Friston