## 1. Diffusion MRI fiber tracking

`Diffusion MRI fiber tracking uses local fiber directions measured at each voxel to track the trajectory of a white matter pathway.`

The axonal directions allow for tracking the trajectories of fiber bundles. The tracking methods can be categorized into deterministic fiber tracking and probabilistic fiber tracking.

## 2. Deterministic fiber tracking

Susumu Mori proposed the FACT method in 1999 [1], which is one of the most popular deterministic fiber tracking approaches. Dr. Basser proposed to use the Euler method for solving ordinary differential equation [2]. Deterministic fiber tracking uses a “deterministic” approach to delineate the fiber trajectory. It starts with a seed point in the white matter and follows local fiber directions (both anterograde and retrograde) in a recursive, step-by-step process until the termination criteria are met. The criteria can include an angular threshold, anisotropy threshold, or anatomical prior. The calculation does not involve any random parameter and thus every time a track from the same seed point, the algorithm will give an identical trajectory.

Deterministic fiber tracking is often done as follows:

`1. Start at a point in the white matter region`
`2. Propagate in one direction with a step size`
`3. Estimate the next propagation direction and repeat 2 until a termination criteria is met`
`4. Redo 1-3 but propagate at the opposite direction.`

source: http://jmahaffy.sdsu.edu/courses/f00/math122/lectures/num_method_diff_equations/nummethod_diffeq.html

Figure source [3]

There are numerous variants of the deterministic fiber tracking, and they can be further classified by the following feature.
• Seeding point: voxel center, sub-voxel
• Propagation: fixed steps, variable step, bidirectional
• Direction estimation: nearest, interpolation, spline
• Termination: FA, angular threshold, anatomical information

There are parameters affecting tracking results.
• Number of seeds placed
• Step size
• Angular threshold
• Anisotropy threshold
• Smoothing
• Minimum/Maximum length allowed
Fiber tracking can make use of a specific region configuration to select tracks of interest or remove false connections.

The following is a list of the region types.
• region of interest (ROI): select tracks passing the region
• seed region: the region to place the seeds
• region of avoidance (ROA): delete tracks passing the region
• ending region: select tracks that end in the region
• the terminative region, tracking mask: terminate tracking if the tracks enter the region
Suggested region combinations
• Whole brain white matter seeding + ROI
• Whole brain white matter seeding + ending regions
• Seeding at target white matter pathways + ROI

### Significance

Deterministic fiber tracking provides a way to do the in-vivo virtual dissection of the brain fiber pathways. It further gives rise to structural connectomics and network-based analysis. The trajectories can be used to sample FA, ADC and allows for track-specific analysis.

Limitations
1. The tracking error accumulates throughout the tracking process.
2. Problems of false continuation and premature termination.
3. The connecting count between two brain regions has poor reproducibility (ICC < 0.5)
4. The crossing-branching problem
source: https://www.nature.com/articles/s41467-017-01285-x/figures/7
Higher angular resolution cannot help distinguish crossing from branching fiber geometry. Crossing and branching fibers generate identical diffusion MRI. A fiber tracking cannot guarantee to capture the ground truth even it has no angular error. This indicates that A fiber tracking algorithm based on local fiber directions has an intrinsic limitation that affects its accuracy.

Recital
1. Deterministic fiber tracking generates a fiber track from a seeding point.
2. The propagation direction is decided by the local fiber orientation.
3. The termination criteria including angular threshold and anisotropy threshold determine when the tracking should stop.

Questions
1. In whole brain fiber tracking, tracks with a longer length usually have more track counts. Why?
2. Does fiber count from fiber tracking inform any biophysics? Why or why not?
3. Numerical analysis shows that RK4 is more accurate than the Euler method for solving ODE. Does this conclusion also apply to diffusion MRI fiber tracking? Why or why not?
4. A study uses a uniform whole brain seeding and fiber tracking to study the connecting tracks between any two regions. The study found significantly higher tracks count connecting two distant regions. Why?
5. What is the difference between the seed region and the region of interest? How to assign them?
6. How to assign ROI/ROA/seed/end region to find the connection between region A and region B in the brain?
7. If we set region A as the seed region and region B as the ending region, does this find tracks ending in both regions?

## 3. Probabilistic fiber tracking

Probabilistic fiber tracking is mostly the same as the deterministic fiber tracking except that there is a random process designed in the propagation direction. As a result, every time a track is generated the same seed point, the algorithm may give a different result. The most popular probabilistic tracking approach is the "probtrackx" in FSL (64% of clinical non-tensor diffusion MRI publications, according to [4]). The method models propagation direction as a distribution. In each tracking step, the algorithm draws a sample from the distribution to propagate the fiber track. The termination is determined by an angular threshold.

source: http://users.fmrib.ox.ac.uk/~behrens/fdt_docs/fdt_probtrack.html

### Significance

Probabilistic fiber tracking iterates all possible trajectories and provides a simulated distribution of the fiber pathways, which can be used to define brain connectivity.

### Limitations

1. Probabilistic fiber tracking may produce mostly false connections.
2. The link to biophysics is weak.

### Performance comparison

In an open competition in 2015 (http://www.tractometer.org/ismrm_2015_challenge/results)[6], deterministic fiber tracking achieved the highest valid connection (could be understood as accuracy) while probabilistic fiber tracking performed badly. However, deterministic fiber tracking missed several small connections, whereas probabilistic fiber tracking found all possible connections. This clearly presented their different applications.

The average accuracy of fiber tracking is around 50%
The average accuracy of DTI fiber tracking is around 60%

source: https://www.nature.com/articles/s41467-017-01285-x/figures/4

source: https://www.nature.com/articles/s41467-017-01285-x/tables/1

Deterministic fiber tracking can be viewed as a maximum likelihood estimation of the fiber trajectories. It aims to find the most probable track of the fiber pathways. Probabilistic fiber tracking aims to explore the empirical distribution of all possible trajectories of the fiber pathways. The distribution can be formulated as a measurement of connectivity. These two approaches have different aims, and depending on the applications, one may work better than another. There is no absolute superiority of one over another [7].

## 5. Exercise

Open the HCP1021.2mm.fib.gz file included in the DSI Studio package (or from https://pitt.box.com/v/HCP1021-2mm) to workout the following:

### Tract Arcuate Fasciculus

• Place ROI's on Brocca's area:
• Open triangularis and opercularis using atlas and merge both regions.
• Place ROI on Wernicke's area:
• Open superior, middle and inferior temporal gyrus using atlas, and merge the regions.
• Check Parameters.
• Click Fiber Tracking.
• Tract Dissection:
• Select, delete, cut, undo, and redo functions, cut.
• Select AF as a seed:
• Use previously created AF and convert the tract to an ROI using "Tract as ROI function".
• Click fiber tracking.
• Use tractography atlas to tract AF.
• Use autotracking function to tract AF.

### Tract Frontal Aslant Tract

• Drawing three regions manually and place as seed, ROA, and ROI.
• Use modify functions: enlarge, smooth.
• Use Prunning function to decrease noise.
• Fiber Dissection:
• Select, delete, angular selection.
• Use flip x function to move regions to opposite side.
• Tract right FAT.

### Visualization and figure creation

• Use of Surface.
• 3D screen copy to clipboard.
• Assign track color.

## 6. Reference

[1] Mori, S., Crain, B.J., Chacko, V.P., van Zijl, P.C., 1999. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Ann Neurol 45, 265-269.
[2] Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., Aldroubi, A., 2000. In vivo fiber tractography using DT-MRI data. Magn Reson Med 44, 625-632.
[3] "Diffusion MRI: Theory, Methods, and Applications", First Edition, Edited by Derek K. Jones, Oxford University Press.
[4] Abhinav, Kumar, et al. "Advanced diffusion MRI fiber tracking in neurosurgical and neurodegenerative disorders and neuroanatomical studies: A review."Biochimica et Biophysica Acta (BBA)-Molecular Basis of Disease 1842.11 (2014): 2286-2297.
[5] Smith, Stephen M., et al. "Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data." Neuroimage 31.4 (2006): 1487-1505.
[6] Maier-Hein, Klaus H., Peter F. Neher, Jean-Christophe Houde, Marc-Alexandre Côté, Eleftherios Garyfallidis, Jidan Zhong, Maxime Chamberland et al. "The challenge of mapping the human connectome based on diffusion tractography." Nature Communications 8, no. 1 (2017): 1349.
[7] Sarwar, T., Ramamohanarao, K., & Zalesky, A. (2018). Mapping connectomes with diffusion MRI: deterministic or probabilistic tractography?. Magnetic resonance in medicine.
[8] Differential Tractography as a Track-Based Biomarker for Neurodegeneration, Fang-Cheng Yeh, Islam M. Zaydan, Valerie R. Suski, David Lacomis, R. Mark Richardson, Joseph C. Maroon, Jessica Barrios-Martinez, bioRxiv 576025; doi: https://doi.org/10.1101/576025