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Glossary
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========
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This page tries to explain some may be uncommon terms related to this project.
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Voxel and Cell
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--------------
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- 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.
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- Cell - In a 3D regular grid the volume enclosed by eight neigboring voxels forming a cube.
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Partial Volume Effect
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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.
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------------------------------------------------------------------------
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Medical Abbreviations
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For an overview on brain anatomy, you should have a look at http://www.healcentral.org/content/6831/Anatomy%20of%20Brain.ppt
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| LCS, CSF | Liquor cerebrospinalis or Cerebrospinal fluid |
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| WM | White Matter |
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| GM | Gray Matter |
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| MRI | Magnetic Resonance Imaging |
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| dwMRI, dMRI | Diffussion weighted MRI |
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| DTI | Diffusion Tensor Imaging |
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| CNG,CG | WM Bundle - Cingulum |
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| CC | WM Bundle - Corpus Callosum |
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| FMaj | WM Bundle - Forceps Major |
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| FMin | WM Bundle - Forceps Minor |
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| CST | WM Bundle - Cortico Spinal Tract |
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| FA | [Diffusion Index](DiffusionIndices) - Fractional Anisotropy |
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| GFA | Diffusion Index - Generalized Fractional Anisotropy |
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| LA | [Diffusion Index](DiffusionIndices) - Linear Anisotropy |
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| RD | Diffusion Index - Radial Diffusivity |
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| MD | Diffusion Index - Mean Diffusivity |
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| ADC | Diffusion Index - Apparent Diffusion Coefficients |
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------------------------------------------------------------------------
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Diffusion Tensor
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----------------
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A second order Diffusion Tensor in three dimensions is a essentially a 3x3 matrix *attempting to model* the diffusion process:
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$$ \\underline{D}=\\left(\\begin{smallmatrix}D\_{xx} & D\_{xy} & D\_{xz}\\\\D\_{yx} & D\_{yy} & D\_{yz}\\\\D\_{zx} & D\_{zy} & D\_{zz}\\end{smallmatrix}\\right) $$
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based on this matrix there are multiple [diffusion indices](DiffusionIndices) 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:
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|-------|---------------|---------------------------|--------------------|------------------------|
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| order | \# components | \# independent components | \# SH coefficients | \# even SH coefficents |
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| 0 | 1 | 1 | 1 | 1 |
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| 1 | 3 | 3 | 4 | 3 |
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| 2 | 9 | 6 | 9 | 6 |
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| 3 | 27 | 10 | 16 | 10 |
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| 4 | 81 | 15 | 25 | 15 |
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| 5 | 243 | 21 | 36 | 21 |
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| 6 | 729 | 28 | 49 | 28 |
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| 7 | 2187 | 36 | 64 | 36 |
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| 8 | 6561 | 45 | 81 | 45 |
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| k | | | $(k+1)^2$ | (k+1)(k+2)/2 |
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