Russ/David,
My take on Russ' question is different. My interpretation was that Russ
is asking about which of the specific mapping algorithms available for
either group or individual fMRI mapping should be used. I'm going to
just include the relevant excerpt from the online ref manual
(http://brainmap.wustl.edu/caret/html/map_fmri_to_surface/map_fmri_to_surface_dialog.html#MappingAlgorithms),
because at least some caret-users may find it useful:
*
*Mapping Algorithms*
*Average Nodes* - This algorithm results in the node being assigned
the average of the voxel it falls within and the voxels its
neighboring nodes fall within.
*Average Voxel* - This algorithm results in the node being assigned
the average of the voxel it falls within and neighboring voxels. The
neighboring voxels are determined with the "Neighbors" parameter.
*Gaussian *-* *Weights surface node's metric value based on local
surface orientation. The functional metric for each surface node is a
weighted sum of the values for nearby voxels. The weighting factor is
a gaussian along the direction of the local surface normal (plus a
cutoff at specified upper and lower bounds) multiplied by a gaussian
in the plane tangential to the surface normal. For these calculations,
the surface normal of each node is averaged with those of immediately
neighboring nodes to reduce local surface irregularities.
*Maximum Voxel* - This algorithm results in the node being assigned
the maixmum of the voxel it falls within and neighboring voxels. The
neighboring voxels are determined with the "Neighbors" parameter.
*MCW Brainfish* - For each voxel within Max Distance of a surface
node, assigns that voxel's value to the closest node. If the same
node is closest to multiple voxels, then that node is assigned the
most positive value; if no values were positive, the most negative
value is assigned. If Splat Factor >= 1, any neighboring nodes not
closest to a voxel are assigned the average of the non-zero values of
its neighbors.
*Mapping Algorithm Parameters*
*Neighbors* - This parameter is used to select neighboring voxels for
some of the mapping algorithms. For a voxel at location (i, j, k) and
a neighbors parameter "n", the voxels used would be the subvolume (i -
n, j - n, k - sn) to (i + n, j + n, k + n).
*Sigma Norm* - lower numbers emphasize data closer to the surface
(Gaussian Algorithm only).
*Sigma Tang* - lower numbers emphasize only nearby data on the surface
(Gaussian Algorithm only).
*Norm Below Cutoff* - excludes data below the surface outside cutoff
(Gaussian Algorithm only).
*Norm Above Cutoff* - excludes data above the surface outside cutoff
(Gaussian Algorithm only).
*Tang Cutoff* - excludes data along the surface outside cutoff
(Gaussian Algorithm only).
*Max Distance* - Maximum distance when finding nodes for a voxel (MCW
Brainfish Algorithm only).
*Splat Factor* - Depth of neighbor nodes (MCW Brainfish Algorithm only).
*
Since the excerpt above was written, enclosing voxel was added; it is
just average voxel with 0 neighbors.
Regarding strengths and weaknesses: Without passing judgment on any of
the methods, I'll just state that here at wustl.edu, users almost always
use the enclosing voxel algorithm, because they do their stats in
volume-land and want Caret to mess with the values as little as
possible. In some specific cases, it makes sense to use enclosing voxel
and use metric smoothing on the surface (Attributes: Metric: Clustering
and Smoothing); however, as far as I know, the smoothing algorithms
constrain the smoothing by ordinal neighbor relationships only -- not
by, say, a geodesic distance kernel, which is a feature I'm guessing
we'll need in the not-too-distant future.
But there are many intelligent people who advocate using not only voxels
that intersect with the fiducial surface, but also any voxels that lie
along the surface normal throughout the cortical thickness.
Specifically, users who have Freesurfer orig and pial surfaces can use
AFNI's 3dVol2Surf for this purpose.
DVE would argue that one achieve similar results using our Gaussian
algorithm, which effectively builds an ellipsoid around each node,
weighting the voxels closest to the node highest, those most distant
lowest. While this is true, 3dVol2Surf has some other options that our
Gaussian option doesn't really support, that may be useful in specific
situations.
My *own* ideas on this subject (not necessarily that of DVE or our lab)
lean toward sticking with the enclosing voxel and letting whatever
smoothing/averaging happen in surface-land (i.e., smudge in 2D -- not
3D). This makes an accurate fiducial surface critical. (Freesurfer
users should average their pial and orig coords to approximate our
fiducial.)
For group data, the most conservative (minimal smudging, extent of
activation region minimized) method is AFM using the enclosing voxel
algorithm (a current wustl.edu favorite). If you want to show a more
liberal/probabilistic view of your region, consider MFM, but stick with
enclosing voxel (let the MFM do the smudging for you -- not the mapping
algorithm). If you're new to these methods, I'd try both and view the
surfaces with the volumes and decide which you believe best represents
whatever it is you want to show. DVE's PALS paper discusses these issues.
For individual data, I'm currently favoring sticking with enclosing
voxel; not fussing over the fact that I'm not letting nearby voxels
'vote'; and counting on the fact that a real effect will affect
neighboring nodes, so that the surface area of the supra-threshold
cluster exceeds some threshold determined to be the type II cut-off.
Some real effects will be smaller than that threshold, but this is the
price we pay to minimize type I error. It is possible that my surface
could fail to intersect with some real effects, but I don't think this
will happen often. Even less often will my surface intersect with
draining blood vessels.
Here are some relevant issues from an AFNI boot camp slide I came across
while preparing for this week's advanced fMRI course at MCW:
http://afni.nimh.nih.gov/pub/dist/edu/latest/suma/Surface-Cross-Subject_files/Slide0023.gif
While my answer probably went far beyond the scope of your original
question, these issues are worthy of discussion. I would add that I'd
rank choice of mapping algorithm well below choice of registration
algorithm -- certainly in the case of surface-based registration, but
perhaps volume-based registration, as well -- in terms of source or
error/distortion/noise.
While it doesn't directly address the subject of mapping algorithms,
Jörn Diedrichsen's just-published "Neural Correlates of Reach Errors"
paper is well worth a read:
http://www.jneurosci.org/cgi/content/full/25/43/9919
Donna
On 10/31/2005 06:44 PM, David Van Essen wrote:
Russ,
I am guessing (hoping) that your query is addressed mainly at the
distinction between 'Average Fiducial Mapping (AFM)' vs.
'Multi-Fiducial Mapping (MFM)', which are the two prime approaches we
currently recommend for mapping to the PALS atlas. If so, I posted a
response to Mike Fox last week (Oct 26th) that addresses this
question. However, it was buried in with several other issues, so I
have excerpted it below.
There are other mapping options in Caret besides AFM and MFM, and
other issues besides what is covered below, so if this doesn't answer
your questions, fire away again.
David
On Oct 31, 2005, at 6:20 PM, Russ Poldrack wrote:
Hi CARETeers - I have a question regarding algorithms for surface
mapping (in this case, mapping group data to the PALS atlas). I
can't seem to find any particular guidance regarding the strengths
and weakness of the various surface mapping algorithms. Can one of
you provide some suggestions regarding algorithm choice, or point
me to a resource that describes this issue in more detail?
cheers
russ
From Mike Fox:
The question I had concerned the validity of mapping to 12
individuals, then averaging those results, as compared to mapping just
once to the average anatomy of the 12 individuals (a new function of
caret). The two do not always give the same result, and I was
wondering if you felt one was superior to the other and why. I know
that volume space atlas registration has adopted the second approach
(ie data is warped to a single atlas which is the average of multiple
subjects anatomy), but this does not necessarily make it superior.
DVE response:
For starters, it's useful to review what I said about this topic in
the Discussion of the PALS paper:
In order to interpret the results of MFM, it is important to consider
several underlying assumptions. Without access to the individual
structural and fMRI data in any given study, it is impossible to work
backwards from volume-averaged group data to determine what the actual
pattern would be in any individual. Hence, the activations seen on any
of the individual PALS-B12 surfaces do not reflect a pattern in fact
attributable to any of the actual fMRI subjects. Nor do they
necessarily reflect the pattern that would have arisen in the 12
subjects whose structural data contributed to the atlas if they had
been tested using the same fMRI paradigm. MFM does provide an
objective strategy for estimating both the region of most likely
activation and a plausible upper bound on the total extent of
activation. This constitutes an important advance over the common
current practice of mapping volume-averaged results onto a
single-subject atlas.
In many situations, it is appropriate to map group-average data using
both AFM and MFM. The two mapping methods yield similar but not
identical spatial patterns and are inherently complementary. AFM is
conceptually simpler and allows readout of values at each surface node
that correspond to a particular voxel value. MFM provides a more
objective assessment of the most likely spatial distribution on the
atlas surface.
-----
In short, I contend that MFM is a superior way to estimate the most
likely spatial location of regions likely to have been modulated in
any given paradigm. AFM can give significant biases in spatial
localization, depending on the nature and location of the data.
However, a price is paid in terms of relating the surface node values
in an MFM map to the voxel values in the volume. In some situations
that's pretty important, but in others it may be largely irrelevant.
These issues are truly complex, as they are intimately linked to the
nature of structural and functional variability and what is really
meant by corresponding locations in different individual hemispheres.
I hope this is helpful. If you have further comments, questions, or
discussion points, let me know.
David
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