Tractography: Difference between revisions
put Mathematics section below MRI technique, which actually describes what the technology is. Cleaned up some formatting and grammar, added wikilinks. Inserted "unref section" template in MRI techniques. |
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== Mathematics == |
== Mathematics == |
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Using [[Diffusion MRI|diffusion tensor MRI]], one can measure the [[Diffusion MRI#ADC|apparent diffusion coefficient]] at each [[voxel]] in the image, and after multilinear regression across multiple images, the whole diffusion tensor can be reconstructed.<ref name=":0">{{cite journal | |
Using [[Diffusion MRI|diffusion tensor MRI]], one can measure the [[Diffusion MRI#ADC|apparent diffusion coefficient]] at each [[voxel]] in the image, and after multilinear regression across multiple images, the whole diffusion tensor can be reconstructed.<ref name=":0">{{cite journal | vauthors = Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A | title = In vivo fiber tractography using DT-MRI data | journal = Magnetic Resonance in Medicine | volume = 44 | issue = 4 | pages = 625–32 | date = October 2000 | pmid = 11025519 | doi = 10.1002/1522-2594(200010)44:4<625::AID-MRM17>3.0.CO;2-O }}</ref> |
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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: |
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: |
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we can solve for <math> \mathbf{r}(s) </math> given the data for <math> \mathbf{u}_1(s) </math>. This can be done using numerical integration, e.g., using [[Runge–Kutta]], and by interpolating the principal [[eigenvector]]s. |
we can solve for <math> \mathbf{r}(s) </math> given the data for <math> \mathbf{u}_1(s) </math>. This can be done using numerical integration, e.g., using [[Runge–Kutta]], and by interpolating the principal [[eigenvector]]s. |
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Tractography is subject to several limitations.<ref name="ChallengeNatComm2017">{{cite journal | |
Tractography is subject to several limitations.<ref name="ChallengeNatComm2017">{{cite journal | vauthors = Maier-Hein KH, Neher PF, Houde JC, Côté MA, Garyfallidis E, Zhong J, Chamberland M, Yeh FC, Lin YC, Ji Q, Reddick WE, Glass JO, Chen DQ, Feng Y, Gao C, Wu Y, Ma J, Renjie H, Li Q, Westin CF, Deslauriers-Gauthier S, González JO, Paquette M, St-Jean S, Girard G, Rheault F, Sidhu J, Tax CM, Guo F, Mesri HY, Dávid S, Froeling M, Heemskerk AM, Leemans A, Boré A, Pinsard B, Bedetti C, Desrosiers M, Brambati S, Doyon J, Sarica A, Vasta R, Cerasa A, Quattrone A, Yeatman J, Khan AR, Hodges W, Alexander S, Romascano D, Barakovic M, Auría A, Esteban O, Lemkaddem A, Thiran JP, Cetingul HE, Odry BL, Mailhe B, Nadar MS, Pizzagalli F, Prasad G, Villalon-Reina JE, Galvis J, Thompson PM, Requejo FS, Laguna PL, Lacerda LM, Barrett R, Dell'Acqua F, Catani M, Petit L, Caruyer E, Daducci A, Dyrby TB, Holland-Letz T, Hilgetag CC, Stieltjes B, Descoteaux M | display-authors = 6 | title = The challenge of mapping the human connectome based on diffusion tractography | journal = Nature Communications | volume = 8 | issue = 1 | pages = 1349 | date = November 2017 | pmid = 29116093 | pmc = 5677006 | doi = 10.10387/s41467-017-01285-x }}</ref> |
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==See also== |
== See also == |
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* [[Connectome]] |
* [[Connectome]] |
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* [[Diffusion MRI]] |
* [[Diffusion MRI]] |
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* [[Connectogram]] |
* [[Connectogram]] |
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==References== |
== References == |
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{{Reflist}} |
{{Reflist}} |
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[[Category:Magnetic resonance imaging]] |
[[Category:Magnetic resonance imaging]] |
Revision as of 17:47, 8 September 2018
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 tensor imaging. The results are presented in two- and three-dimensional images called tractograms.
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.
MRI technique
Tractography is performed using data from diffusion tensor imaging. 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. 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, 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 anisotropy of 0 corresponds to a perfect sphere, whereas 1 is an ideal linear diffusion. Well-defined tracts have FA larger than 0.20. 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:
- Red indicates directions in the X axis: right to left or left to right.
- Green indicates directions in the Y axis: posterior to anterior or from anterior to posterior.
- Blue indicates directions in the Z axis: foot-to-head direction or vice versa.
The technique is unable to discriminate the "positive" or "negative" direction in the same axis.
Mathematics
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 easily 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.
Tractography is subject to several limitations.[2]
See also
References
- ^ a b Basser PJ, Pajevic S, Pierpaoli C, Duda J, Aldroubi A (October 2000). "In vivo fiber tractography using DT-MRI data". Magnetic Resonance in Medicine. 44 (4): 625–32. doi:10.1002/1522-2594(200010)44:4<625::AID-MRM17>3.0.CO;2-O. PMID 11025519.
- ^ Maier-Hein KH, Neher PF, Houde JC, Côté MA, Garyfallidis E, Zhong J, et al. (November 2017). "The challenge of mapping the human connectome based on diffusion tractography". Nature Communications. 8 (1): 1349. doi:10.10387/s41467-017-01285-x. PMC 5677006. PMID 29116093.