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
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 essentially a 3x3 matrix attempting to model the diffusion process:
\underline{D}=\left(\begin{matrix}D_{xx} & D_{xy} & D_{xz}\\D_{yx} & D_{yy} & D_{yz}\\D_{zx} & D_{zy} & D_{zz}\end{matrix}\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 {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 |