Diffusion MRI fiber tracking


Diffusion MRI fiber tracking


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. 


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 streamline fiber tracking based on the Euler method for solving ordinary deferential equation [2]. Currently about 36% of the tractography publications use deterministic fiber tracking [4].



Figure source [3]

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


The 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.

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


Significance

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.

Pros
1. High efficiency and most intuitive approach for tracking fiber bundle
2. Applicable to all diffusion MRI reconstruction methods

Cons

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)

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.

Probabilistic fiber tracking

The most popular probabilistic tracking approach is the "probtrackx" in FSL (64% of clinical non-tensor ediffusion MRI publications, according to [7]). 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.

Pros

1. Higher reproducibility
2. FSL uses it

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

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.

Solution: increase spatial resolution

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.

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 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.

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.

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.

Questions

1. Does fiber count generated from fiber tracking informs any biophysics? Why or why not?
2. Numerical analysis shows that RK4 is more accurate than Euler method for solving ODE. Does this conclusion also apply to diffusion MRI fiber tracking? Why or why not?
3. 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?
4. What is the difference between seed region and region of interest? How to assign them?
5. How to assign ROI/ROA/seed/end region to find the connection between region A and region B in the brain?
6. If we set region A as the seed region and region B as the ending region, does this find tracks ending in both regions?

Exercise

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.
2. Use track editing to select/delete/cut/ tracks (see Tract Editing)
3. Run whole-brain fiber tracking and examine the effect of adding seed region, ROI, ROA, ending region, and terminative region.
4. Use a combination of ROI/ROA/seed region/ending region from an atlas to track corticospinal tracks, arcuate fasciculus.
5. Calculate the length and volume of track trajectories.

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.
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