DMCC GLMs: afni TENTzero, knots, and HDR curves, #2

This post is the second in a series, which begins with this post. In that first post I included examples of the estimated HDR curves for a positive control analysis, one of which is copied here for reference. 

What are the axis labels for the estimated HDR curves? How did we generate them? What made us think about changing them? 

At the first level the (curve) axis label question has a short answer: y-axes are average (across subjects) beta coefficient estimates, x-axes are knots. But this answer leads to another question: how do knots translate into time? Answering this question is more involved, because we can't translate knots to time without knowing both the TR and the afni 3dDeconvolve command. The TR is easy: 1.2 seconds. Listing the relevant afni commands is also easy:

3dDeconvolve \  
 -local_times \  
 -x1D_stop \  
 -GOFORIT 5 \  
 -input 'lpi_scale_blur4_tfMRI_AxcptBas1_AP.nii.gz lpi_scale_blur4_tfMRI_AxcptBas2_PA.nii.gz' \  
 -polort A \  
 -float \  
 -censor movregs_FD_mask.txt \  
 -num_stimts 3 \  
 -stim_times_AM1 1 f1031ax_Axcpt_baseline_block.txt 'dmBLOCK(1)' -stim_label 1 ON_BLOCKS \  
 -stim_times 2 f1031ax_Axcpt_baseline_blockONandOFF.txt 'TENTzero(0,16.8,8)' -stim_label 2 ON_blockONandOFF \  
 -stim_times 3 f1031ax_Axcpt_baseline_allTrials.txt 'TENTzero(0,21.6,10)' -stim_label 3 ON_TRIALS \  
 -ortvec motion_demean_baseline.1D movregs \  
 -x1D X.xmat.1D \  
 -xjpeg X.jpg \  
 -nobucket  
 
3dREMLfit \
 -matrix X.xmat.1D \
 -GOFORIT 5 \
 -input 'lpi_scale_blur4_tfMRI_AxcptBas1_AP.nii.gz lpi_scale_blur4_tfMRI_AxcptBas2_PA.nii.gz' \
 -Rvar stats_var_f1031ax_REML.nii.gz \
 -Rbuck STATS_f1031ax_REML.nii.gz \
 -fout \
 -tout \
 -nobout \
 -verb

Unpacking these commands is not so easy, but I will try to do so here for the most relevant parts; please comment if you spot anything not quite correct in my explanation.

First, the above commands are for the Axcpt task, baseline session, subject f1031ax (aside: their data, including the event timing text files named above, is in DMCC13benchmark). The 3dDeconvolve command has the part describing the knots and HDR estimation; I included the 3dREMLfit call for completeness, because the plotted estimates are from the Coef sub-bricks of the STATS image (produced by -Rbuck).

Since this is a control GLM in which all trials are given the same label there are only three stimulus time series: BLOCKS, blockONandOFF, and TRIALS (this is a mixed design; see introduction). The TRIALS part is what generates the estimated HDR curves plotted above, as defined by TENTzero(0,21.6,10).

We chose TENTzero instead of TENT for the HDR estimation because we do not expect anticipatory activity (the trial responses should start at zero) in this task. (see afni message board, e.g., here and here) To include the full response we decided to model the trial duration plus at least 14 seconds (not "exactly" 14 seconds because we want the durations to be a multiple of the TENT duration). My understanding is that it's not a problem if more time than needed is included in the duration; if too long the last few knots should just approximate zero. I doubt you'd often want to use a duration much shorter than that of the canonical HRF (there's probably some case when that would be useful, but for the DMCC we want to model the entire response).

From the AFNI 3dDeconvolve help: 

'TENT(b,c,n)': n parameter tent function expansion from times b..c after stimulus time [piecewise linear] [n must be at least 2; time step is (c-b)/(n-1)]

 

You can also use 'TENTzero' and 'CSPLINzero',which means to eliminate the first and last basis functions from each set. The effect of these omissions is to force the deconvolved HRF to be zero at t=b and t=c (to start and and end at zero response). With these 'zero' response models, there are n-2 parameters (thus for 'TENTzero', n must be at least 3).

The first TENTzero parameter is straightforward: b=0 to start at the event onset.

For the trial duration (c), we need to do some calculations. Here, the example is the DMCC Axcpt task, which has a trial duration of 5.9 seconds, so the modeled duration should be at least 14 + 5.9 = 19.9 seconds. That's not the middle value in the TENTzero command, though.

For these first analyses we decided to have the TENTs span two TRs (1.2 * 2 = 2.4 seconds), in the (mostly) mistaken hope it would improve our signal/noise, and also to make the file sizes and GLM estimation speeds more manageable (which it does). Thus, c=21.6, the shortest multiple of our desired TENT duration greater than the modeled duration (19.9/2.4 = 8.29, rounded up to 9; 9*2.4 = 21.6). 

Figuring out n requires a bit of mind bending but less calculation; I think the slide below (#5 in afni06_decon.pdf) helps: in tent function deconvolution, the n basis functions are divided into n-1 intervals. In the above calculations I rounded 8.29 up to 9; we want to model 9 intervals (of 2.4 s each). Thus,  n = 10 basis functions gives us the needed n-1 = 9 intervals.

Recall that since we're using TENTzero, the first and last tent functions are eliminated. Thus, having n=10 means that we will get 10-2=8 beta coefficients ("knots") out of the GLM. These, finally, are the x-axes in the estimated GLM curves above: the knots at which the HDR estimates are made, of which there are 8 for Axcpt. 

(Aside: 0-based afni can make some confusion for those of us more accustomed to 1-based systems, especially with TENTzero. The top plots put the value labeled as #0_Coef at 1; a point is added at 0=0 since TENTzero sets the curves to start at zero. I could also have added a zero for the last knot (9, for this Axcpt example), but did not.)

These GLMs seem to be working fine, producing sensible HDR estimates. We've been using these results in many analyses (multiple lab members with papers in preparation!), including the fMRIprep and HCP pipeline comparisons described in previous posts. We became curious, though, if we could set the knot duration to the TR, rather than twice the TR (as done here): would the estimated HDR then follow the trial timing even more precisely? In the next posts(s) I'll describe how we changed the GLMs to have the knot duration match the TR, and a (hopefully interesting) hiccup we had along the way.

UPDATE 4 January 2021: Corrected DMCC13benchmark openneuro links.

DMCC GLMs: afni TENTzero, knots, and HDR curves, #1

One of the things we've been busy with during the pandemic-induced data collection pause is reviewing  the DMCC (Dual Mechanisms of Cognitive Control; more descriptions here and here) project GLMs: did we set them up and are we interpreting them optimally? 

We decided that the models were not quite right, and are rerunning all of them. This post (and its successors) will describe how the original GLMs were specified, why we thought a change was needed, what the change is, and how the new results look. The posts are intended to summarize and clarify the logic and process for myself, but also for others, as I believe many people find modeling BOLD responses (here, with afni 3dDeconvolve TENTs) confusing.

 

I won't just start explaining the DMCC GLMs however, because they're complex: the DMCC has a mixed design (task trials embedded in long blocks), and we're estimating both event-related ("transient") and block-related ("sustained") responses. If you're not familiar with them, Petersen and Dubis (2012) review mixed block/event fMRI designs, and Figure 1 from Visscher, et. al (2003) (left) illustrates the idea. In addition to the event and block regressors we have "blockONandOFF" regressors in the DMCC, which are intended to capture the transition between the control and task periods (see Dosenbach et. al (2006)).

We fit many separate GLMs for the DMCC, some as controls and others to capture effects of interest. For these posts I'll describe one of the control analyses (the "ONs") to make it a bit more tractable. The ON GLMs include all three effect types (event (transient), block (sustained), blockONandOFF (block start and stop)), but do not distinguish between the trial types; all trials (events) are given the same label ("on"). The ON GLMs are a positive control; they should show areas with changes in activation between task and rest (30 seconds of fixation cross before and after task blocks). For example, there should be positive, HRF-type responses in visual areas, because all of our task trials include visual stimuli.

Below is an example of the estimated responses from our original ONs GLMs (generated by R knitr code similar to this). The GLMs were fit for every voxel individually, then averaged within the Schaefer, et al. (2018) parcels (400x7 version); these are results for four visual parcels and volumetric preprocessing. These are (robust) mean and SEM over 13 participants (DMCC13benchmark). The results have multiple columns both because there are four DMCC tasks (Axcpt (AX-CPT), Cuedts (Cued task-switching), Stern (Sternberg working memory), and Stroop (color-word variant)), and because of the mixed design, so we generate estimates for both event/transient (lines) and sustained (blue bars) effects (blockONandOFF are not included here).

The line graphs show the modeled response at each time point ("knot"). Note that the duration (and so number of estimated knots) for each task varies; e.g., Stroop has the shortest tasks and Stern the longest. (We set the modeled response to trial length + 14 seconds.)

The double-peak response shape for Axcpt, Cuedts, and Stern is expected, as the trials have two stimuli slides separated by a 4 second ITI; the Stroop response should resemble a canonical HRF since each trial has a single stimulus and is short. The task timing and some sample trials are shown below (this is  Figure 1 in a preprint (accepted version) which has much more task detail; see also the DMCC55B description). 

So far, so good: the estimated responses for each task have a sensible shape, reflecting both the HRF and task timing. But what exactly is along the x-axis for the curves? And how did we fit these GLMs, and then decide to change them a bit? ... stay tuned.

later posts in this series: #2

UPDATE 4 January 2021: Corrected DMCC13benchmark openneuro links.