Local tractography

Overview

Questions

• What input data does a local tractography method require?
• Which steps does a local tractography method follow?

Objectives

• Understand the basic mathematical principle behind local tractography
• Be able to identify the necessary elements for a local tractography method

Local tractography

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Local tractography algorithms follow 2 general principles:

1. Estimate the fiber orientation, and
2. Follow along these orientations to generate/propagate the streamline.

Streamline propagation is, in essence, a numerical analysis integration problem. The problem lies in finding a curve that joins a set of discrete local directions. As such, it takes the form of a differential equation problem of the form:
Streamline propagation differential equation

where the curve \(r(s)\) needs to be solved for.

To perform conventional local fiber tracking, three things are needed beyond the propagation method itself:

1. A method for getting local orientation directions from a diffusion MRI dataset (e.g. diffusion tensor).
2. A set of seeds from which to begin tracking.
3. A method for identifying when to stop tracking.

Different alternatives have been proposed for each step depending on the available data or computed features.

When further context data (e.g. tissue information) is added to the above to perform the tracking process, the tracking method is considered to fall into the Anatomically-Constrained Tractography (Smith et al. 2012) family of methods.

Key Points

• Local tractography uses local orientation information obtained from diffusion MRI data
• Tractography requires seeds to begin tracking and a stopping criterion for termination