Standard tractography on in-silico phantom

Blurring fiber orientations using TODI or dMRI simulation

Fibertube tracking

Example of peaks extracted from ODFs.

Standard tractography on in-silico phantom

Fibertube tracking

Tracking

Standard tractography on in-silico phantom

Fibertube tracking

Fibertube tracking

Standard tractography on in-silico phantom

The result is scored for bundle connectivity and coverage.

Standard tractography on in-silico phantom

Tracking directly on fibertubes (streamlines with diameter). At each step, the next direction is picked randomly from within a blurring sphere.

Fibertube tracking

Standard tractography on in-silico phantom

Resolution can be "increased" by reducing the radius of the blurring sphere.

Fibertube tracking

Fibertube tracking

Standard tractography on in-silico phantom

The result is scored, this time for individual fibertube connectivity.

Fibertube tracking – Picking the next direction

Intersection volumes:

■ : ~2um²

Random distribution:

■ : 100%

The intersection between the sphere and the orange segment is ~2um².�It has a 100% chance of being picked as the next direction.

Fibertube tracking – Picking the next direction

Intersection volumes:

■ : ~1.6um²

■ : ~0.4um²

Random distribution:

■ : 80%

■ : 20%

After multiple steps with the same result, we now have a different situation.

We now have an 80% chance of choosing the orientation of ■ and a 20% chance of choosing the orientation of ■.

Fibertube tracking – Picking the next direction

To respect the Θ angle constraint, fibertube segments are filtered prior to selection. In this situation, both ■ and ■ are filtered out.

Fibertube tracking – Picking the next direction

The only stopping criterion is the absence of fibertube segments intersecting with the sphere. (After filtering for Θ constraint)

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In this situation, because ■ was picked at the previous step, there is now nowhere to go. This is the end of the streamline.

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If the step size is larger than the sphere's radius, there will be a higher chance of early stoppage. These two parameters should be chosen wisely.

Fibertube tracking – Picking the next direction

By using a very large sphere and step size, we can "blur" the data more.

Fibertube tracking – Picking the next direction

Fibertube tracking – Picking the next direction

By using a sphere of radius and step size = ~0, we could achieve a theoretically "perfect" tracking of the fibertubes.

Fibertube tracking – Picking the next direction

Fibertube tracking – Validation of the tractogram

Each streamline is associated with an "Termination fibertube segment", which is the closest fibertube segment to its before-last coordinate. We then define the following terms:

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"Valid Connection" (VC): A streamline whose termination fibertube segment is the final segment of the fibertube in which is was originally seeded.

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"Invalid Connection" (IC): A streamline whose termination fibertube segment is the start or final segment of a fibertube in which is was not seeded.

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"No Connection" (NC): A streamline whose termination fibertube segment is not the start or final segment of any fibertube.

Seeded fibertube

Non-seeded fibertube

Fibertube tracking – Validation of the tractogram

Fibertube tracking can also assess how well the produced streamline "reconstructs" its associated fibertube. It computes the absolute error of streamline coordinates.

Properties:

• No connection (the streamline did not reach the end segment of its fibertube)
• Resolution-wise no connection
• MAE (\) : ~3um
• ED (\) : 10 um

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The endpoint distance is the distance between the last coordinate of the streamline and the last coordinate of its parent fibertube

Properties:

• Valid connection
• Resolution-wise valid connection
• MAE (\) : 0um
• ED (\) : 0um

​

Fibertube tracking – Validation of the tractogram

Fibertube tracking – Validation of the tractogram

Properties:

• Invalid connection (the streamline reached the start or end segment of another fibertube)
• Resolution-wise valid connection AND invalid connection
• MAE (\) : ~2um
• ED (\) : 5um

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Ground-truth Orientation

Distribution

Directions:

22% 23% 40% 15%

Probability distribution:

Each direction is always a valid, existing direction of the ground-truth fibertubes. Very powerful and appears to converge towards an optimal trajectory at extremely small scale and step size.

ftODF

22% 23% 40% 15%

45%

40%

15%

Ground-truth Orientation distribution

ftODF as SF

Slight loss of information when approximating on sphere vertices

Almost equivalent to TODI performed locally during tracking. The only difference is that TODI is typically weighted by the length of each segment, while ftODF is weighted by the intersection volume. This ftODF can be used for probabilistic sampling, as well as deterministic peak extraction

ftODF as SH

Fin de présentation

Images

Fibertube Segment

Fibertube

Centerline

Diameter

Inter-segment Gap

Inter-segment Superposition

Fibertube Segment

T

T’

T

T’

Radius

Radius

VC

IC

NC

Tracker

ODFPropagator(AbstractPropagator)

DataVolume

• Coordinates tracking
• Evaluates stopping criteria

• Selects a propagation direction from an ODF
• Runge-Kutta integration

• Manages resolution and space attributes
• Converts and returns data at coordinates

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Tracker

FibertubePropagator(AbstractPropagator)

FibertubeDataVolume(DataVolume)

Unchanged

• Uses ground-truth orientation distribution instead of ODF

• Stores fibertubes instead of a grid of ODFs
• Returns ground-truth orientation distribution given a position and blurring sphere

Tracker

ODFPropagator(AbstractPropagator)

ftODFDataVolume(FibertubeDataVolume)

Unchanged

Unchanged

• Stores fibertubes instead of a grid of ODFs
• Computes and returns ftODF given a position and blurring sphere.

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