What are different ways to determine centroids of fMRI activation, their drawbacks and perks?

Question

I'm reading an older article on bilingualism (Kim, Relkin, Lee, & Hirsch, 1997) for a seminar. They were interested in the spatial separation of two languages in early and late bilinguals. They determined activated regions and their overlap in two conditions and across two groups.

To determine these areas, they first excluded all voxels where BOLD response difference to baseline was not above their empirically derived false positive rate (p<0.0005) and then used all these voxels as if they had the same activation to determine the "centre-of-mass".

They then calculated the distance between the centroids in the two conditions to measure spatial separation and counted the overlapping voxels.

I have some issues with this method:

• it seems as if they're throwing away a lot of information by discarding all voxels where activity was not above chance level and maybe more importantly by treating all significantly activated voxels as the same even though there may be significant differences in their activation level
• minor: it's volumetric, not mass, so it should be centre of volume, right? It may be a misunderstanding of the workings of fMRI on my part.

They also demonstrated that the derived distance held up well over two orders of magnitude in significance level, but still they didn't differentiate between highly and not-so-highly-but-still-significantly activated voxels. Is this still state-of-the-art?

My questions:

• What are different ways to calculate centroids without discarding so much information but still backing up the conclusion inferentially (some sort of spatial confidence area?)?

• What are their drawbacks (my lecturer says they all have some, so you can just as well use the above-mentioned multistage method, but this seems like the easy way out)?

• What is a well-tested method to test spatial separation of activity for two conditions? I'm not asking about demonstrating functional separation, but once you don't treat voxels as on-and-off anymore, calculating degree of overlap becomes less trivial.

References

• Kim, K.H.S. and Relkin, N.R. and Lee, K.M. and Hirsch, J. (1997). Distinct cortical areas associated with native and second languages, Nature. FREE PDF

Answer 1

This question gets close to something that might alternatively be posted to stats.stackoverflow.com. Personally, I've always felt that application of Null-Hypothesis Significance Testing (NHST) methods to neuroimaging data does a particularly good job of highlighting their scientific deficiencies.

Personally, these days I'd use Generalized Additive Modelling (GAM) to analyze data from an individual's scan and if aggregating multiple spatially normalized scans I'd use Generalized Additive Mixed effects Modelling (GAMM). In both approaches, I'd use an AIC-adjusted likelihood ratio to evaluate the strength of evidence for differences amongst groups/conditions in the activity patterns discerned by GAM. A posteriori investigation of any evidence-supported differences can be achieved by visualization and parametric bootstrapping of confidence intervals.

If you really want to explicitly evaluate evidence for a group difference in the distance between activation areas, then one approach is to assume an a priori model for the activation, say a mixture of two trivariate gaussians with a parameter that specifies their separation, then use something like hierarchical Bayesian modelling to establish credible intervals on the difference between groups on the separation parameter.

Answer 2

Great question!

To start, you are absolutely right-- a 1997 article on fMRI is considered very old as far as the field is concerned. Statistical techniques have improved dramatically since then so, while I haven't read the article in question, it's safe to assume that there are probably lots of things they would do differently if the study was conducted today. In fact, there are often quite a few ways of analyzing the same data; some of my answers below reflect my own experience using AFNI (SPM users may use different techniques).

it seems as if they're throwing away a lot of information by discarding all voxels where activity is not above chance level and maybe more importantly by treating all significantly activated voxels as the same even though there may be significant differences in their activation level

Following the standard mass-univariate approach to fMRI, there is not much you can do about throwing away voxels that aren't below alpha level. Not doing so would inflate your Type I error rate. There are alternatives to the mass-univariate approach, such as multi-voxel pattern analysis (MVPA), but each technique has its own strengths and weaknesses.

As far as treating all significant voxels the same-- that's not quite true. They usually are treated the same qualitatively-- that's just how classical hypothesis testing works. A p-value less than alpha means you can reject the null, otherwise you can't. There's no middle ground. Besides, voxel activations are all relative anyway (using the cognitive subtraction technique), so absolute activation levels are not always informative. However, you can use activation levels to determine the centroid! So let me jump to that:

What are different ways to calculate centroids without discarding so much information but still backing up the conclusion inferentially (some sort of spatial confidence area?)?

After performing a mass GLM to determine significant voxels, voxels can be clustered. In AFNI, this is done using a k-neighbors approach; e.g. if I set my cluster size to k=20, all voxels that don't belong to a cluster of minimum 20 contiguous, significant voxels will be eliminated.

The center of each cluster is most often reported as the peak activation in the cluster (see? not all activations are treated equally). Sometimes, it is reported as the geometric center of mass-- and yes, that's volume, not real mass. Peak is usually more informative because it's more likely that the task your measuring is functionally localized at the peak, rather than the center of mass. However, center of mass may give you a better idea of the spatial extent of your cluster. There are probably better justifications, but that's what jumps to mind...

What is a good method to test spatial separation of activity for two conditions? I'm not asking about demonstrating functional separation, but once you don't treat voxels as on-and-off anymore, calculating degree of overlap becomes less trivial.

In general, spatial separation is usually not important. Some functional regions are much larger than others-- there may be 'little' functional difference between voxels that are largely separated in the motor cortex. But the same spatial separation between voxels of two different cytoarchitectonic structures may have radically different functions. I may be missing the point here though, if so, please clarify and I'll try to help...