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. 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.
Deterministic fiber tracking uses a “deterministic” approach to delineate the fiber trajectory. It starts with a seed point in the white matter and propagates along local fiber directions (both anterograde and retrograde) in a recursive, step-by-step process until the termination criteria are met. The criteria can include 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 identical trajectory.
Probablistic 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.
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.
In an open competition in 2015 (http://www.tractometer.org/ismrm_2015_challenge/results), 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.
Susumu Mori proposed the FACT method in 1999 , which is one of the most popular deterministic fiber tracking approaches. Dr. Basser proposed streamline fiber tracking based on the Euler method for solving ordinary deferential equation . Currently about 36% of the tractography publications use deterministic fiber tracking .
Figure source 
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
Fiber tracking is usually conducted with a specific region configuration that 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
terminative region, tracking mask: terminate tracking if the tracks enter the region
Deterministic fiber tracking provides a way to do 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.
1. The crossing-branching (or kissing-branching) problem. Fiber tracking cannot distinguish crossing fibers from branching fibers.
2. The tracking error accumulates throughout the tracking process.
3. Problems of false continuation and premature termination.
4. The connecting count between two brain regions has poor reproducibility (ICC < 0.5)
Currently, the most popular tracking approach is "probtrackx" in FSL (64% of clinical non-tensor ediffusion MRI publications, according to ). The method models propagation direction as a distribution, and the algorithm draws a sample from the distribution during track propagation. The termination is determined by an angular threshold.
Probabilistic fiber tracking iterates all possible trajectories and provide the empirical distribution of the fiber pathways, which can be used to define brain connectivity.
1. Probabilistic fiber tracking may produce a large amount of false connections.
2. The link to biophysics is weak.
1. Numerical analysis shows that RK4 is more accurate than Euler method in solving ODE. Does this conclusion also apply to diffusion MRI fiber tracking? Why or why not?
2. A study uses 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?
3. What is the difference between seed region and region of interest? How to assign them?
4. How to setup ROI/ROA/seed/end to find the connection between region A and region B in the brain?
5. If we set region A as the seed region and region B as the ending region, does this find tracks ending in both regions?
 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.
1. Open a FIB file and run fiber tracking (see Fiber Tracking). Change parameters such as anisotropy threshold, turning angle, ..etc and observe the effect.
 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.
 "Diffusion MRI: Theory, Methods, and Applications", First Edition, Edited by Derek K. Jones, Oxford University Press.
 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.
 Smith, Stephen M., et al. "Tract-based spatial statistics: voxelwise analysis of multi-subject diffusion data." Neuroimage 31.4 (2006): 1487-1505.