# 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