Tractography | |
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![]() Tractography of human brain | |
Purpose | used to visually represent nerve tracts |
In neuroscience, tractography is a 3D modeling technique used to visually represent nerve tracts using data collected by diffusion MRI. [1] It uses special techniques of magnetic resonance imaging (MRI) and computer-based diffusion MRI. The results are presented in two- and three-dimensional images called tractograms. [2]
In addition to the long tracts that connect the brain to the rest of the body, there are complicated neural circuits formed by short connections among different cortical and subcortical regions. The existence of these tracts and circuits has been revealed by histochemistry and biological techniques on post-mortem specimens. Nerve tracts are not identifiable by direct exam, CT, or MRI scans. This difficulty explains the paucity of their description in neuroanatomy atlases and the poor understanding of their functions.
The most advanced tractography algorithm can produce 90% of the ground truth bundles, but it still contains a substantial amount of invalid results. [3]
Tractography is performed using data from diffusion MRI. The free water diffusion is termed "isotropic" diffusion. If the water diffuses in a medium with barriers, the diffusion will be uneven, which is termed anisotropic diffusion. In such a case, the relative mobility of the molecules from the origin has a shape different from a sphere. This shape is often modeled as an ellipsoid, and the technique is then called diffusion tensor imaging [4] . Barriers can be many things: cell membranes, axons, myelin, etc.; but in white matter the principal barrier is the myelin sheath of axons. Bundles of axons provide a barrier to perpendicular diffusion and a path for parallel diffusion along the orientation of the fibers.
Anisotropic diffusion is expected to be increased in areas of high mature axonal order. Conditions where the myelin or the structure of the axon are disrupted, such as trauma, [5] tumors, and inflammation reduce anisotropy, as the barriers are affected by destruction or disorganization.
Anisotropy is measured in several ways. One way is by a ratio called fractional anisotropy (FA). An FA of 0 corresponds to a perfect sphere, whereas 1 is an ideal linear diffusion. Few regions have FA larger than 0.90. The number gives information about how aspherical the diffusion is but says nothing of the direction.
Each anisotropy is linked to an orientation of the predominant axis (predominant direction of the diffusion). Post-processing programs are able to extract this directional information.
This additional information is difficult to represent on 2D grey-scaled images. To overcome this problem, a color code is introduced. Basic colors can tell the observer how the fibers are oriented in a 3D coordinate system, this is termed an "anisotropic map". The software could encode the colors in this way:
The technique is unable to discriminate the "positive" or "negative" direction in the same axis.
Using diffusion tensor MRI, one can measure the apparent diffusion coefficient at each voxel in the image, and after multilinear regression across multiple images, the whole diffusion tensor can be reconstructed. [1]
Suppose there is a fiber tract of interest in the sample. Following the Frenet–Serret formulas, we can formulate the space-path of the fiber tract as a parameterized curve:
where is the tangent vector of the curve. The reconstructed diffusion tensor can be treated as a matrix, and we can compute its eigenvalues and eigenvectors . By equating the eigenvector corresponding to the largest eigenvalue with the direction of the curve:
we can solve for given the data for . This can be done using numerical integration, e.g., using Runge–Kutta, and by interpolating the principal eigenvectors.
Anisotropy is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance, refractive index, conductivity, and tensile strength.
Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.
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Diffusion-weighted magnetic resonance imaging is the use of specific MRI sequences as well as software that generates images from the resulting data that uses the diffusion of water molecules to generate contrast in MR images. It allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and non-invasively. Molecular diffusion in tissues is not random, but reflects interactions with many obstacles, such as macromolecules, fibers, and membranes. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state. A special kind of DWI, diffusion tensor imaging (DTI), has been used extensively to map white matter tractography in the brain.
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Fractional anisotropy (FA) is a scalar value between zero and one that describes the degree of anisotropy of a diffusion process. A value of zero means that diffusion is isotropic, i.e. it is unrestricted (or equally restricted) in all directions. A value of one means that diffusion occurs only along one axis and is fully restricted along all other directions. FA is a measure often used in diffusion imaging where it is thought to reflect fiber density, axonal diameter, and myelination in white matter. The FA is an extension of the concept of eccentricity of conic sections in 3 dimensions, normalized to the unit range.
The following outline is provided as an overview of and topical guide to brain mapping:
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High definition fiber tracking (HDFT) is a tractography technique where data from MRI scanners is processed through computer algorithms to reveal the detailed wiring of the brain and to pinpoint fiber tracts. Each tract contains millions of neuronal connections. HDFT is based on data acquired from diffusion spectrum imaging and processed by generalized q-sampling imaging. The technique makes it possible to virtually dissect 40 major fiber tracts in the brain. The HDFT scan is consistent with brain anatomy unlike diffusion tensor imaging (DTI). Thus, the use of HDFT is essential in pinpointing damaged neural connections.
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