<p>Great question!</p>

<p>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).</p>

<blockquote>
  <p>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</p>
</blockquote>

<p>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.</p>

<p>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:</p>

<blockquote>
  <p>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?)?</p>
</blockquote>

<p>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.</p>

<p>The center of each cluster is most often reported as the <em>peak</em> 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...</p>

<blockquote>
  <p>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.</p>
</blockquote>

<p>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...</p>

CC BY-SA 3.0
2012-02-04T13:46:40.163Z
Thanks for your reply, Jeff. This is pretty much what the authors did and what I took issue with though (except for using clustering which doesn't seem to be a remedy for "throwing away information", might even be worse). I know how classical hypothesis testing works, but if the research question is about the separation of areas (not about "is this voxel active", which it never should be), then I think this multistage analysis discards information that could have served to improve the estimate. Maybe this can not be resolved in a frequentist approach.
Ruben
CC BY-SA 3.0
2012-02-04T18:07:43.113Z
I have a lot of issues with 'standard' fMRI analysis myself; but I don't know that this is one of them. H1 is "is this brain region involved in the function we are testing". The activation level doesn't tell you "how much" a region is involved in a function, it's simply a matter of power to detect whether H1 is true. Activation level can be heavily dependent upon a lot of experimental design issues-- e.g., event vs block related, canonical HRF vs temporal derivative, etc. If you're interested in level of activation, you can use a parametric design-- but that requires a different analysis.
Jeff
CC BY-SA 3.0
2012-02-03T03:55:02.680Z
2012-02-03T03:55:02.680Z
Jeff
<p>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. </p>

<p>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. <em>A posteriori</em> investigation of any evidence-supported differences can be achieved by visualization and parametric bootstrapping of confidence intervals.</p>

<p>If you <em>really</em> want to <em>explicitly</em> 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.</p>

CC BY-SA 3.0
2012-01-31T10:09:12.207Z
Thanks for your answer. I realize this is also a statistical question, but because it seems to be a common method in neuroscience even though the deficits are obvious, I thought I'd ask here. Their scans weren't spatially normalized, they looked at intraindividual differences (conditions were within-subject) which makes more sense I suppose (or do I misunderstand you?). What do you consider the reason data like this is not commonly analyzed in the fashion you propose (I've been told it isn't, this old article maybe doesn't do the field justice)?
Ruben
CC BY-SA 3.0
2012-02-03T02:38:35.677Z
@Ruben The reason is that as a discipline, cognitive science is stuck in a "jack of all trades, master of none" approach to training and conduct of research. That is, researchers try to take responsibility for too many roles in research (theoretician, empiricist, statistician, etc) and in doing so cannot provide deep expertise throughout. The superior alternative is to emulate the approach taken in physics and work in teams of specialists, including data analysts with PhDs in statistics who make their career contributing to statistical rigor and innovation.
Mike Lawrence
CC BY-SA 3.0
2012-01-29T20:43:42.193Z
2012-04-27T03:15:53.163Z
2012-04-27T03:15:53.163Z
Mike Lawrence
<p>I'm reading an older article on bilingualism (Kim, Relkin, Lee, &amp; 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.</p>

<p>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&lt;0.0005) and then used all these voxels as if they had the same activation to determine the "centre-of-mass".</p>

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

<p>I have some issues with this method:</p>

<ul>
<li>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 </li>
<li>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.</li>
</ul>

<p>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?</p>

<h3>My questions:</h3>

<ul>
<li>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?)?  </li>
<li><p>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)?</p></li>
<li><p>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.</p></li>
</ul>

<h3>References</h3>

<ul>
<li>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, <em>Nature</em>. <a href="http://www.colorado.edu/MCDB/MCDB3650/SecondLanguage.pdf" rel="nofollow">FREE PDF</a></li>
</ul>

CC BY-SA 3.0
2012-12-23T02:46:27.460Z
This wasn't crying out for an edit, but it'd be nice to give this question additional attention.
Chuck Sherrington
CC BY-SA 3.0
2012-02-05T01:25:25.000Z
Thanks for getting involved with the site. It's great to have active researchers contributing.
Jeromy Anglim
<neuroscience><language><neuroimaging><fmri>
What are different ways to determine centroids of fMRI activation, their drawbacks and perks?
Ruben
# What are different ways to determine centroids of fMRI activation, their drawbacks and perks?

(Asked by: username_0 on 2012-01-29)

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](http://www.colorado.edu/MCDB/MCDB3650/SecondLanguage.pdf)

**Tags:** neuroscience, language, neuroimaging, fmri

> **Comments:**
> **username_2**: Thanks for getting involved with the site. It's great to have active researchers contributing.  
> **username_1**: This wasn't crying out for an edit, but it'd be nice to give this question additional attention.  

---

## 2 answers

### Answer by username_4 on 2012-01-29. Score: 5 | Accepted answer

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.

> **Comments:**
> **username_0**: Thanks for your answer. I realize this is also a statistical question, but because it seems to be a common method in neuroscience even though the deficits are obvious, I thought I'd ask here. Their scans weren't spatially normalized, they looked at intraindividual differences (conditions were within-subject) which makes more sense I suppose (or do I misunderstand you?). What do you consider the reason data like this is not commonly analyzed in the fashion you propose (I've been told it isn't, this old article maybe doesn't do the field justice)?  
> **username_4**: @username_0 The reason is that as a discipline, cognitive science is stuck in a "jack of all trades, master of none" approach to training and conduct of research. That is, researchers try to take responsibility for too many roles in research (theoretician, empiricist, statistician, etc) and in doing so cannot provide deep expertise throughout. The superior alternative is to emulate the approach taken in physics and work in teams of specialists, including data analysts with PhDs in statistics who make their career contributing to statistical rigor and innovation.  

---

### Answer by username_3 on 2012-02-03. Score: 4

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...

> **Comments:**
> **username_0**: Thanks for your reply, username_3. This is pretty much what the authors did and what I took issue with though (except for using clustering which doesn't seem to be a remedy for "throwing away information", might even be worse). I know how classical hypothesis testing works, but if the research question is about the separation of areas (not about "is this voxel active", which it never should be), then I think this multistage analysis discards information that could have served to improve the estimate. Maybe this can not be resolved in a frequentist approach.  
> **username_3**: I have a lot of issues with 'standard' fMRI analysis myself; but I don't know that this is one of them. H1 is "is this brain region involved in the function we are testing". The activation level doesn't tell you "how much" a region is involved in a function, it's simply a matter of power to detect whether H1 is true. Activation level can be heavily dependent upon a lot of experimental design issues-- e.g., event vs block related, canonical HRF vs temporal derivative, etc. If you're interested in level of activation, you can use a parametric design-- but that requires a different analysis.  

---

