# 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 |