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Glossary

This page tries to explain some may be uncommon terms related to this project.

Voxel and Cell

  • Voxel - The center point of the volume region where the data was measured (averaged). Sometimes also the region itself. The positions in the grids are the voxels.
  • Cell - In a 3D regular grid the volume enclosed by eight neigboring voxels forming a cube.

Partial Volume Effect

The partial volume effect occurs when a single voxel contains a mixture of multiple tissue values which may result in blurring or dimming parts. Other effects may be that tracked fibers are discontinous or broken.


Medical Abbreviations

For an overview on brain anatomy, you should have a look at http://www.healcentral.org/content/6831/Anatomy%20of%20Brain.ppt

LCS, CSF Liquor cerebrospinalis or Cerebrospinal fluid
WM White Matter
GM Gray Matter
MRI Magnetic Resonance Imaging
dwMRI, dMRI Diffussion weighted MRI
DTI Diffusion Tensor Imaging
CNG,CG WM Bundle - Cingulum
CC WM Bundle - Corpus Callosum
FMaj WM Bundle - Forceps Major
FMin WM Bundle - Forceps Minor
CST WM Bundle - Cortico Spinal Tract
FA Diffusion Index - Fractional Anisotropy
GFA Diffusion Index - Generalized Fractional Anisotropy
LA Diffusion Index - Linear Anisotropy
RD Diffusion Index - Radial Diffusivity
MD Diffusion Index - Mean Diffusivity
ADC Diffusion Index - Apparent Diffusion Coefficients

Diffusion Tensor

A second order Diffusion Tensor in three dimensions is a essentially a 3x3 matrix attempting to model the diffusion process:

$$ \underline{D}=\left(\begin{smallmatrix}D_{xx} & D_{xy} & D_{xz}\\D_{yx} & D_{yy} & D_{yz}\\D_{zx} & D_{zy} & D_{zz}\end{smallmatrix}\right) $$

based on this matrix there are multiple diffusion indices defined. They may or may not exist also for higher order tensors (FA versus GFA). A symmetric tensor of order k and dimension d has {{latex(${d+k-1}\choose{k})}} different independent components. The following lists some numbers for d=3:

order # components # independent components # SH coefficients # even SH coefficents
0 1 1 1 1
1 3 3 4 3
2 9 6 9 6
3 27 10 16 10
4 81 15 25 15
5 243 21 36 21
6 729 28 49 28
7 2187 36 64 36
8 6561 45 81 45
k $(k+1)^2$ (k+1)(k+2)/2