LaplaceGrid

Generating the grid file for solving Laplace's equation

minclaplace requires a volume with the boundaries defined correctly to work. There are four types of boundaries (three of them required):

1. Outside: the area the streamlines move to.
2. Inside: the area the streamlines move from.
3. Middle: the area in between outside and inside where the streamlines will be defined.
4. Resistive: a boundary that is ignored (this was a new addition of our 2008 paper).

The easiest way to generate these boundaries is to begin with an atlas that is aligned to each image. Then the make_laplace_grid command can be used to generate the grid from that atlas. This is done by providing both the atlas and a csv file describing the mapping of the atlas to the grid. The csv file looks as follows:

,Structure,right label,left label,hierarchy,tissue type,boundary
1,amygdala,51,151,,GM,inside
2,anterior commissure: pars anterior,115,215,,WM,inside
3,anterior commissure: pars posterior,23,103,,WM,inside
4,basal forebrain,52,152,,GM,inside
...
98,Cingulate cortex: area 24b,27,172,Cingulate region,GM,middle
99,Cingulate cortex: area 24b',28,173,Cingulate region,GM,middle
100,Cingulate cortex: area 25,29,178,Cingulate region,GM,middle adjacent resistive
101,Cingulate cortex: area 29a,30,179,Cingulate region,GM,middle adjacent resistive

Each row corresponds to an anatomical region in the atlas, with the columns representing the row number (optional), the structure name, the label number in the right and left hemispheres, a definition of the hierarchy within which that structure sits (optional), and the boundary definition.

The default mapping is assumed to be outside. In this example of the mouse cortex the cortical regions, such as cingulate area 24b, are then defined as middle, since that is where we want to measure cortical thickness from. There is one additional boundary definition possible: middle adjacent resistive. This represents an area of the atlas where the equation should be solved, but the inside label adjacent to it will be converted to be resistive instead. Best illustrated with an example:

In this case, we want the corpus callosum underneath part of the cingulate to be resistive, otherwise we get weird streamlines that turn a sharp corner, which does not accurately represent what we know the cortical columns to be doing. Note that part of the amygdala and the colliculi were set to be resistive in mapping file as well.

With the csv file in place, it can converted to a grid suitable for minclaplace as follows:

 make_laplace_grid --binary_closing -l \
 Dorr_2008_Steadman_2013_Ullmann_2013_on_NRXN1a_v1_labels.mnc \
 Dorr_2008_Steadman_2013_Ullmann_2013_mapping_of_labels.csv \
 output_grid.mnc

This command outputs the grid for the left hemisphere (-l, -r or --right would make it the right hemisphere), adds the optional --binary-closing which runs morphological operators to remove small holes in the cortical boundary definition, then provides the MINC file containing the atlas, the csv file with the mapping definitions as described above, and the output volume.