Hi

On 20 Dec 2006, at 21:15, Stephane Jacobs wrote:

> Hello everyone,
>
> In the process of trying to understand cluster thresholding, I  
> played around
> with some different and sometimes non-sense values both for the Z  
> score and
> the P value thresholds.
>

Good, but be aware that if you're using non-sense values don't expect  
to be able to interpret results ...

> My understanding of the cluster thresholding is that it comprises 2  
> steps:
> 1) a Z score threshold is apply to every voxel,  keeping only the  
> ones that
> pass the threshold.

yep

> 2) the map obtained for the first step is thresholded again using  
> the chosen
> P value, which determines a limit size for the clusters to be  
> considered
> significant. This size is obtained from the gaussian field theory,  
> but it's
> unclear to me how exactly the P value and the size correspond, if  
> anybody
> wants to take a shot at explaining this... (this is actually my first
> question here I guess!)
>

Well, the probability of one or more super-thresholded cluster is  
approximated by the expected Euler characteristics (number of blobs -  
number of holes). This approximation is something like

E(EC) = c * (Z^2-1) * exp (-1/2*Z^2)

where c is some constant that depends on the smoothness, the size of  
the search region and Z is your threshold. This approximation only  
makes sense when EC is less than 1 and only becomes somewhat accurate  
once EC get's close to 0...

If you plot such a curve you'll find that EC is approaching 0 as Z  
gets large _or_ as Z gets close to +-1. For high Z the EC basically  
is the number of blobs only - our implementation deals nicely with  
this case, For low Z you'd also need to include the number of holes.  
For Z->0 the EC should be negative. Using the FSL implementation will  
not give interpretable results in this range...

>
> So, in one of my thresholding experimentations, I have thresholded  
> my data
> to Z = 0 and P = 1.0, which means to me NO THRESHOLDING at all -  
> all the
> voxels pass the Z score threshold (0), and the P value allows all the
> clusters as small as a single voxel to be considered significant.

Not really, for reasons outlined above... the expression for p is not  
analytic, it's approximated by the expected EC which is not valid in  
this range if you only count the number of blobs...

Bottom line: GRF via E(EC) makes sense only at reasonable smoothness  
levels and for Z >> 1.
cheers
christian

> This is a
> stupid thresholding, but I just wanted to check that I had understood
> everything properly. Thus, I expected to get a really noisy map,  
> with the
> whole brain lighting up (nice for Christmas...). To my wonder, I  
> get totally
> reasonable patterns of activations!
> Of importance is that what I describe here happens when I do a
> paired-comparison analysis. When I just contrast each of my  
> experimental
> conditions vs. rest, I do get a nice Christmas tree, as expected.  
> Could
> anybody tell me the reason for that?

>
> Thanks a lot for any help,
>
> Stephane

--
  Christian F. Beckmann
  Oxford University Centre for Functional
  Magnetic Resonance Imaging of the Brain,
  John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK
  Email: [log in to unmask] - http://www.fmrib.ox.ac.uk/~beckmann/
  Phone: +44(0)1865 222551 Fax: +44(0)1865 222717