Voxel wise comparison (Voxel Based Morphometry or VBM) acorss subjects in fMRI studies

I am new to fMRI field and seek apology for this very basic question.
In many fMRI studies like This Study a voxel wise comparison is made across subjects and controls . As we know that dataset in fMRI in the form of 3D matrix like Subjects x TimePoints x Voxels that is on each person we have bunch of time points and on each time points we have voxel values as voxel is unit of measurement in bold signal in the brain that is brain is divided into small cubicle voxels.

My specific question No.1 is that if we have a dataset consisting of 20 control and 15 subjects with 5000 voxels and 200 time points on all persons then we will have two 3D matrices in following form

For Subjects: 15 x 200 x 5000

For controls: 20 x 200 x 5000

Now how voxel wise comparison would be made between two subjects as these datasets are not balanced in persons or first dimension.

My specific question No.2 is that how regions are compared between those two group like this has been done on page 2(13).

My Understanding

For question No.1 my understanding is that a single matrix is made for each group by reducing the person(subject/control) dimension that is we will have two 200 x500 matrices average over individuals in each matrix and then the voxel wise comparison will be made using t test in any two voxel as each voxel will have 200 time points.

For question No.2 my understanding is that for a typical brain area like “Right thalamus” A group of voxel called cluster like 147 as used in the paper is organized and then voxel vectors are formed for both groups averaged over individuals like out of 147 voxel vector a typical voxel vector will have 200 values and that will be compared.

lastly some times the volumes are reported in the specific brain region like “Right thalamus” in cc and again my question is that how theses volumes are computed?

So I am totally messed up here and need guidance here in my understanding ?

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Hi Naseer,

I have no experience with VBM, but I can address a couple points here.

First, VBM is an analysis of structural, not functional, MRI data. In the paper you link, they took T1-weighted and T2-weighted structural images.

As I described in How fMRI data is organized, the data will be organized in 3D volumes per-subject, not a single voxels-by-timepoints-by-subjects volume. The paper describes a normalization procedure, targeting the SPM-included MNI template, and calculating the proportion of total gray matter appearing in each voxel for each subject. That is, a single volume of this measure was calculated for each subject.

Some prior knowledge of VBM seems to be assumed by the paper, but my guess is that a parcellation of the MNI template (an atlas) was chosen (possibly one is bundled with SPM, but there are a number you can explore using the OBART). From this atlas, the indices of the voxels labeled as a given region (e.g. right thalamus) could then be used to calculate the average or total gray matter volume in that region.

This is straightforward in Python (and I expect similarly so in MATLAB):

import nibabel as nb
atlas_img = nb.load('atlas.nii.gz')  # 3D volume of labels (usually integers)
test_img = nb.load('sub-01_graymatter.nii.gz')  # 3D volume of measure interest
# Assume we have a constant R_THALAMUS corresponding
# to the atlas label for right thalamus
total_size = test_img.get_data()[atlas_img.get_data() == R_THALAMUS].sum() # scalar

So now what you’d be able to calculate is one measure per subject per area of interest, which would be a 2D matrix. From here you can run your ANOVA with any confounds you may want.

Again, I have not done a VBM analysis, so I would treat this as a broad context of how to think about volumes and subjects and measures. I may be very wrong in details. Hopefully someone with a bit more VBM experience will be able to correct me if I’ve strayed too far.