| ... | ... | @@ -6,8 +6,8 @@ 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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- 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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- **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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| ... | ... | @@ -19,10 +19,11 @@ The partial volume effect occurs when a single voxel contains a mixture of multi |
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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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|----------|-----------------------------------------------|
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| LCS, CSF | Liquor cerebrospinalis or Cerebrospinal fluid |
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| WM | White Matter |
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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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| ... | ... | @@ -44,11 +45,11 @@ For an overview on brain anatomy, you should have a look at http://www.healcentr |
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Diffusion Tensor
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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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A second order diffusion tensor in three dimensions is 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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$` \underline{D}=\left(\begin{matrix}D_{xx} & D_{xy} & D_{xz}\\D_{yx} & D_{yy} & D_{yz}\\D_{zx} & D_{zy} & D_{zz}\end{matrix}\right) `$
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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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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 $`{d+k-1}\choose{k}`$ different independent components. The following lists some numbers for $`d=3`$:
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|-------|---------------|---------------------------|--------------------|------------------------|
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| ... | ... | @@ -62,6 +63,6 @@ based on this matrix there are multiple [diffusion indices](DiffusionIndices) de |
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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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| k | | | $`(k+1)^2`$ | $`(k+1)(k+2)/2`$ |
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