...  @@ 6,8 +6,8 @@ This page tries to explain some may be uncommon terms related to this project. 
...  @@ 6,8 +6,8 @@ This page tries to explain some may be uncommon terms related to this project. 

Voxel and Cell


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.


 **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.


 **Cell**  In a 3D regular grid the volume enclosed by eight neigboring voxels forming a cube.






Partial Volume Effect


Partial Volume Effect







...  @@ 19,10 +19,11 @@ The partial volume effect occurs when a single voxel contains a mixture of multi 
...  @@ 19,10 +19,11 @@ The partial volume effect occurs when a single voxel contains a mixture of multi 

Medical Abbreviations


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 


 LCS, CSF  Liquor cerebrospinalis or Cerebrospinal fluid 


 WM  White Matter 


 WM  White Matter 


 GM  Gray Matter 


 GM  Gray Matter 


 MRI  Magnetic Resonance Imaging 


 MRI  Magnetic Resonance Imaging 


 dwMRI, dMRI  Diffussion weighted MRI 


 dwMRI, dMRI  Diffussion weighted MRI 

...  @@ 44,11 +45,11 @@ For an overview on brain anatomy, you should have a look at http://www.healcentr 
...  @@ 44,11 +45,11 @@ For an overview on brain anatomy, you should have a look at http://www.healcentr 

Diffusion Tensor


Diffusion Tensor












A second order Diffusion Tensor in three dimensions is a essentially a 3x3 matrix *attempting to model* the diffusion process:


A second order diffusion tensor in three dimensions is essentially a 3x3 matrix *attempting to model* the diffusion process:






$$ \\underline{D}=\\left(\\begin{smallmatrix}D\_{xx} & D\_{xy} & D\_{xz}\\\\D\_{yx} & D\_{yy} & D\_{yz}\\\\D\_{zx} & D\_{zy} & D\_{zz}\\end{smallmatrix}\\right) $$


$` \underline{D}=\left(\begin{matrix}D_{xx} & D_{xy} & D_{xz}\\D_{yx} & D_{yy} & D_{yz}\\D_{zx} & D_{zy} & D_{zz}\end{matrix}\right) `$






based on this matrix there are multiple [diffusion indices](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+k1}\\choose{k})}} different independent components. The following lists some numbers for d=3:


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 $`{d+k1}\choose{k}`$ different independent components. The following lists some numbers for $`d=3`$:






     


     







...  @@ 62,6 +63,6 @@ based on this matrix there are multiple [diffusion indices](DiffusionIndices) de 
...  @@ 62,6 +63,6 @@ based on this matrix there are multiple [diffusion indices](DiffusionIndices) de 

 6  729  28  49  28 


 6  729  28  49  28 


 7  2187  36  64  36 


 7  2187  36  64  36 


 8  6561  45  81  45 


 8  6561  45  81  45 


 k    $(k+1)^2$  (k+1)(k+2)/2 


 k    $`(k+1)^2`$  $`(k+1)(k+2)/2`$ 








