FA is calculated in every voxel. Typically, for DTI-tracking studies, we are interested in the WM skeleton part of the brain. In humans >5 years old or so, this is well approximated where FA>0.2, and therefore we perform tractography through this region of the brain.
We perform tracking to estimate the most likely location of WM associated with any pair of regions that is input (or, if the number of regions is >2, which it often is, we estimate the same kind of thing for each pair). This gives us a best guess at where WM might be connecting regions, tractographically. The set of voxels that are home to the tracts connecting ROI_A and ROI_B form a new ROI, a WM ROI or what we often call a “WM connection” between ROI_A and ROI_B; perhaps call this WMC_AB. The mean FA of this region is indeed stored in the matrix, at the element intersected by ROI_A’s row/column and ROI_B’s column/row, respectively. But we calculate more than just mean FA in the ROI; we also calculate its standard deviation (sFA matrix), and the 3dTrackID help file describes all the default matrices:
The first *five* matrices are currently (this may change over time):
NT = number of tracks in that WM-ROI
fNT = fractional number of tracks in that WM-ROI, defined as NT
divided by total number of tracts found (may not be relevant)
PV = physical volume of tracks, in mm^3
fNV = fractional volume of tracks compared to masked (internally or
'-mask'edly) total volume; would perhaps be useful if said
mask represents the whole brain volume well.
NV = number of voxels in that WM-ROI.
BL = average length (in mm) of a bundle of tracts.
sBL = stdev of the length (in mm) of a bundle of tracts.
Then, there can be a great variety in the remaining matrices, depending
on whether one is in DTI or HARDI mode and how many scalar parameter
files get input (max is 10). For each scalar file there are two
matrices: first a label (e.g., 'FA') and then an N_ROI-by-N_ROI matrix
of the means of that parameter in each WM-ROI; then a label (here,
would be 'sFA') and then an N_ROI-by-N_ROI matrix of the standard
deviations of that parameter in each WM-ROI.
The goal of all tractography (IMHO) is to esimate the WM most likely associated with a region, or with a pair of regions (with the latter seeming more a more useful application to me). Deterministic and probabilistic tracking are two different flavors of tracking; these are described in detail in the FATCAT*pdf notes and in other places. The deterministic tracking does not take into account the uncertainty information in a tensor estimate, and it is more susceptible to noise effects. The probabilistic tends to be more robust. But each is providing an estimate of WMCs. Because they estimate WMCs differently, each will “paint out” a different looking WMC for a given pair of target regions, in general, and so the average FA over a different set of voxels will likely be different.
Re. Q2: NT is always the number of tracts from tracking, either deterministic or probabilistic. Note that I don’t think this is a useful quantity for quantitative comparisons, but instead it is useful as a check on the algorithm and to provide relative information.
Re. Q3: related to Q2 and to various parts of the FATCAT presentations, I do not agree that one can use the number of tracts (NT) to estimate a “strength” of connection. That would imply that they are a literal analogue/representation of underlying WM, but I don’t see how the could be. They are useful numerical representations of where we think the DTI estimates are providing information of possible connections in the brain-- so maybe we have more confidence where there are lots of tracts compared to where there are few tracts in a given brain-- but I don’t think they should be compared as a contrast between two groups or anything like that. The tract counts are used to find and possibly trim where we think we can locate WM connections, and I think that should be their only purpose. They should be thought of more as “likelihood” indicators, rather than numbers to compare.
The FA has no directionality, so I don’t think it can be interpreted that way. FA is the scaled standard deviation of the eigenvalues of the diffusion tensor. This tends to have some relation to underlying WM: again, where FA>0.2 in humans over 5 is a good map of WM. However, I don’t know that FA can be unambiguously linked to a particular aspect of WM. This Beaulieu (2001) paper:
has nice descriptions of trying to relate DTI parameters-- like FA, and others-- to biology.
Re. Q4: Well, the answer to the previous question relates to my views on what NT and FA do and don’t represent. So, I don’t agree that they both show strength of connection. I think this can be a confusing point because I still read papers that try to refer to NT as a measure of biological strength of connection (and I don’t even know what “strength of connection” of WM means on its own merits!), but I don’t see how one can interpret the quantity like that. Grumble.
FA is a very different quantity, and it might have more biological relation, but there also, things are tricky-- see the above cited paper.
I don’t know that we have any DTI measure which really probes “strength” of connection. To me, NT at best offers “likelihood of connection passing this way” (with allll the caveats about tractography that are well deserved…), and FA offers a measure related to WM properties, sure, but probably not “strength” in terms of bundle diameter or axon count, necessarily. I am sure there are models that aim to relate FA to such WM properties directly, but I would assume those are pretty model-dependent.