Creating Beta Series Correlation Maps

The last few steps for creating beta series correlation maps is practically identical to what we did before with other functional connectivity maps:

1. Load your beta series map into the AFNI interface and set it as the underlay;
2. Click on "Graph" to scroll around to different voxels and examine different timeseries;
3. Once you find a voxel in a region that you are interested in, write out the timeseries by clicking FIM -> Edit Ideal -> Set Ideal as Center; and then FIM -> Edit Ideal -> Write Ideal to 1D File. (In this case, I am doing it for the right motor cortex, and labeling it RightM1.1D.)
4. Note that you can also average the timeseries within a mask defined either anatomically (e.g., from an atlas), or functionally (e.g., from a contrast). Again, the idea is the same as what we did with previous functional connectivity analyses.
5. Use 3drefit to trick AFNI into thinking that your beta series map is a 3d+time dataset (which by default is not what is output by 3dbucket):

3drefit -TR 2 Left_Betas+tlrc

6. Use 3dfim+ to create your beta series correlation map:

3dfim+ -input Left_Betas+tlrc -polort 1 -ideal_file RightM1.1D -out Correlation -bucket RightM1_BetaSeries

7. Convert this to a z-score map using Fisher's r-to-z transformation:

3dcalc -a Corr_subj01+tlrc -expr 'log((1+a)/(1-a))/2' -prefix Corr_subj01_Z+tlrc

8. Do this for all subjects, and use the results with a second-level tool such as 3dttest++.

9. Check the freezer for HotPockets.

That's it; you're done!

Introduction to Beta Series Analysis in AFNI

So far we have covered functional connectivity analysis with resting-state datasets. These analyses focus on the overall timecourse of BOLD activity for a person who is at rest, with the assumption that random fluctuations in the BOLD response that are correlated implies some sort of communication happening between them. Whether or not this assumption is true, and whether or not flying lobsters from Mars descend to Earth every night and play Scrabble on top of the Chrysler Building, is still a matter of intense debate.

However, the majority of studies are not resting-state experiments, but instead have participants perform a wide variety of interesting tasks, such as estimating how much a luxury car costs while surrounded by blonde supermodels with cleavages so ample you could lose a backhoe in there. If the participant is close enough to the actual price without going over, then he -

No, wait! Sorry, I was describing The Price is Right. The actual things participants do in FMRI experiments are much more bizarre, involving tasks such as listening to whales mate with each other*, or learning associations between receiving painful electrical shocks and pictures of different-colored shades of earwax. And, worst of all, they aren't even surrounded by buxom supermodels while inside the scanner**.

In any case, these studies can attempt to ask the same questions raised by resting-state experiments: Whether there is any sort of functional correlation between different voxels within different conditions. However, traditional analyses which average beta estimates across all trials in a condition cannot answer this, since any variance in that condition is lost after averaging all of the individual betas together.

Beta series analysis (Rissman, Gazzaley, & D'Esposito, 2004), on the other hand, is interested in the trial-by-trial variability for each condition, under the assumption that voxels which show a similar pattern of individual trial estimates over time are interacting with each other. This is the same concept that we used for correlating timecourses of BOLD activity while a participant was at rest; all we are doing now is applying it to statistical maps where the timecourse is instead a concatenated series of betas.

Figure 1 from Rissman et al (2004). The caption is mostly self-explanatory, but note that for the beta-series correlation, we are looking at the amplitude estimates, or peaks of each waveform for each condition in each trial. Therefore, we would starting stringing together betas for each condition, and the resulting timecourse for, say, the Cue condition would be similar to drawing a line between the peaks of the first waveform in each trial (the greenish-looking ones).

The first step to do this is to put each individual trial into your model; which, mercifully, is easy to do with AFNI. Instead of using the -stim_times option that one normally uses, instead use -stim_times_IM, which will generate a beta for each individual trial for that condition. A similar process can be done in SPM and FSL, but as far as I know, each trial has to be coded and entered separately, which can take a long time; there are ways to code around this, but they are more complicated.

Assuming that you have run your 3dDeconvolve script with the -stim_times_IM option, however, you should now have each individual beta for that condition output into your statistics dataset. The last preparation step is to extract them with a backhoe, or - if you have somehow lost yours - with a tool such as 3dbucket, which can easily extract the necessary beta weights (Here I am focusing on beta weights for trials where participants made a button press with their left hand; modify this to reflect which condition you are interested in):

3dbucket -prefix Left_Betas stats.s204+tlrc'[15..69(2)]'

As a reminder, the quotations and brackets mean to do a sub-brik selection; the ellipses mean to take those sub-briks between the boundaries specified; and the 2 in parentheses means to extract every other beta weight, since these statistics are interleaved with T-statistics, which we will want to avoid.

Tomorrow we will finish up how to do this for a single subject. (It's not too late to turn back!)

*Fensterwhacker, D. T. (2011). A Whale of a Night: An Investigation into the Neural Correlates of Listening to Whales Mating. Journal of Mongolian Neuropsychiatry, 2, 113-120.

**Unless you participate in one of my studies, of course.

Future Functional Connectivity Tutorials, and Other Updates

A few notes:

1) The previous functional connectivity posts and tutorials are cribbed from Gang Chen's homepage, which is available here. Kind of like the way I crib quotations and passages from authors that no one reads anymore, and then pass it off as my own style to boost my pathologically low self-esteem. Keep in mind that most of these demonstrations deal with a single subject and simplified situations that you probably will not encounter in your research. Given these contrived examples, most of the results generated in these demos are relatively meaningless; it's up to you to learn and understand the concepts, and then apply them to your own data and make your own inferences. My task which I am trying to achieve is, by the power of Youtube tutorials, to make you hear, to make you feel — it is, before all, to make you understand. That — and no more, and it is everything. (That was Conrad, by the way.)

2) A lot of you - I'm talking a LOT of you players - have been making requests for MELODIC tutorials and resting state analyses in FSL. All I can say is, we'll get there, in time. Before that, however, I believe AFNI is better suited for building up one's intuition, and so we will be working through a few more connectivity topics in AFNI - specifically, context-dependent correlations, beta series correlations, and resting state connectivity. After that we will again cover the same concepts, but applied in FSL - by which time, given my glacial pace, either FMRI will have become a passé technique or the Andromeda galaxy will have crashed into us.

3) Recently you may have noticed the "Donate" button on the right sidebar of the blog. This was done at the request of one reader who felt the powerful, irrational urge to loosen his purse-strings and give some alms out of the goodness of his heart, which is located somewhere way, way down there, somewhere nearabouts the cockles. Although I can't fully understand this behavior - even less than I can understand why there is someone who still has purse-strings, or what cockles are, exactly - nevertheless it helps satisfy my cupidity and strokes my ego. Furthermore, in addition to serving Mammon, these tokens of gratitude motivate me to regularly produce new material and, as a bonus, help me to continue procrastinating on my dissertation. Now that's what I call a win-win-win.

4) Also, at least one of you has mailed me a two-pack of Nutella. This has pleased me greatly. My brain needs hazelnut spread for fuel, and the more it has, the hotter and better it burns.

5) If everything goes according to plan, we should cover context-dependent correlations this weekend, beta series correlations next week, and resting-state connectivity the week after that.

Lunch in Paris, dinner in London, comrade.