DTI probabilistic tracking


I am doing DTI analysis by FATCAT and TORTOISE pipeline.
After running 3dTrackID for the Probabilistic tracking, I could get several matrices. FA-based connectivity matrices, Number of streamlines, etc.
I want to ask how these connectivity matrices were calculated between ROIs and also what is the meaning of these matrices.



I think these AFNI Bootcamp lectures on DTI and tracking provide the most comprehensive information:

These slides go with those talks:

afni_open -aw FATCAT_01_background_dti.pdf
afni_open -aw FATCAT_02_dti_tracking_intro.pdf
afni_open -aw FATCAT_03_dti_tracking_funcs.pdf
afni_open -aw FATCAT_04_netw_stats_mvm.pdf
afni_open -aw FATCAT_HO.pdf

… and these papers provide useful descriptions:
Taylor PA, Saad ZS (2013). FATCAT: (An Efficient) Functional And Tractographic Connectivity Analysis Toolbox. Brain Connect. 3, 523–535. doi.org/10.1089/brain.2013.0154

Taylor PA, Chen G, Cox RW, Saad ZS (2016). Open Environment for Multimodal Interactive Connectivity Visualization and Analysis. Brain Connect. 6, 109–121. doi.org/10.1089/brain.2015.0363

Please let me know if you have any questions following from that.


Hi Paul,
AFNI lectures were very helpful for me to understand the concept of DTI.
But I have still some questions which I couldn’t solve from lecture notes.
My main question is for FA connectivity matrix and NT connectivity matrix.

  1. Whole brain FA map can be obtained before tracking process. In order to calculate FA connectivity matrix (ROIs by ROIs), I ran 3dTrackID for probabilistic tracking. Now I can find FA connectivity matrix. For example, if I have a mean FA value between ROI_A and ROI_B from this matrix, this FA value is average value from voxels along the tract? If so, deterministic tracking(one or more streamlines) and probabilistic tracking (volume) provide different mean FA value for the same pair of ROIs?
  2. Is NT calculated the same even in deterministic tracking or probabilistic tracking?
  3. NT connectivity matrix gives straightforwardly the number of streamlines which shows how strong the pair of ROIs are connected each other through white matter. FA connectivity matrix shows how much directionality between ROIs. Do I understand them right way?
  4. For FA connectivity matrix and NT connectivity matrix, why do we consider both differently? For me, both seem to show the strength of connection between ROIs. Is there any proper rationale that we try to see these two differently?

If you can give me answers about these, it will be very helpful.


Hi, Jung-

Re. Q1:
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.


In other probabilistic tractography method, it was applied by sampling 5000 streamline fibers per voxel. For a seed region, 5000 × n fibers were sampled; n is the number of voxels in the region. The number of fibers passing through a given region divided by 5000 × n is calculated as the connectivity probability from the seed region to the given region.

In the 3dTrackID, it used several options : -alg_Thresh_Frac , -alg_Nseed_Vox , and -alg_Nmonte. Is the output NT matrix also normalized by the number of voxels (the size of seed region)?


I am a bit familiar with other (softwares’) tractography methods, but not in detail. Note that many other softwares will have different ways of proceeding, so analogous quantities might have very different calculations/derivations.

I think that approach that you have descriped from another software package is very different than AFNI/FATCAT’s: that other one is starting tracts only from one region and shooting outward to another region. (Note also that I think firing tracts from ROI_A to ROI_B in that case would yield different results than firing from ROI_B to ROI_A, though I think that would not be a desired trait in outputs-- tractography cannot distinguish underlying WM directionality, so its results should not be directionally dependent.)

AFNI/FATCAT’s basically calculates tracts throughout the WM skeleton (where FA>0.2, say), and then finds the subset of tracts from those that connect to both ROI_A and ROI_B. Thus, there is no directionality in discussing results of tracking from ROI_A to ROI_B or from ROI_B to ROI_A (which seems appropriate, to me): there are just tracts between ROI_A and ROI_B. The total number of tracts throughout the whole brain is Nmonte * Nseed_Vox * Nvox. The total number of WB tracking iterations is essentially: Nmonte * Nseed_Vox. The user picks a value Thresh_Frac, which is in range [0, 1], that is the fraction of WB tracking iterations to be used to set the minimum number of tracts to pass through a voxel to keep it within an ROI. Thus, if you do Nmonte = 1000 Monte Carlo iterations of Nseed_Vox = 5 seeds per voxel, giving you essentially 5000 WB tracking iterations, and choose Thresh_Frac = 0.1, then you are going to require 5000*0.1 = 500 tracts that connect ROI_A and ROI_B to pass through a voxel for it to be considered within that ROI_A-to-ROI_B connection (the WMC, as noted in previous email).