Details on the mouse isocortex flatmap: how were the cortical coordinates derived?

As a software engineer of the Blue Brain Project (EPFL, Geneva), I am investigating different ways of creating flat maps for several brain regions of interest.

The process by which a curved coordinate system has been derived for the mouse isocortex is described at pages 6 and 7 of the CCF technical white paper.

Thanks to Laplace’s equation, the isocortex is turned into a foliation “orthogonal to cortical depth” with a top leaf, that is the pia surface, and a bottom leaf, the white matter surface.

The files located in

seem to hold a flattened version of these two surfaces stored in 2-dimensional numpy arrays.

I would be very grateful to you if you could explain to me how these files were generated.

I opened a ticket here https://github.com/AllenInstitute/mouse_connectivity_models/issues/44

where Kameron Harris kindly explained that AIBS scientists did generate these files.

Thanks in advance for your answer.

Best regards,

Luc

Hi Luc.

Thanks to Laplace’s equation, the isocortex is turned into a foliation “orthogonal to cortical depth” with a top leaf, that is the pia surface, and a bottom leaf, the white matter surface.

Once the Laplacian is computed, we loop through every pia surface voxel and compute steepest descent path through the laplaican result until we get to white matter surface. The path is just list of 10 micron voxels. All of the paths are store in files for later reuse.

A 2D view is essentially a lookup table to pia surface voxel.

For the mouse_connectivity_models these are all surface voxel you can see from a dorsal (top-down view).

I am not sure exactly what value they put in their 2D view for “mouse_connectivity_model” as I did not contribute code to that project.

However, in this 2D view: http://connectivity.brain-map.org/projection/experiment/cortical_map/529692491

The process is, for every pixel, look up with surface voxel is associated with. Then using the stored path, find the maximum value through the corresponding “projection density volume” and assign to the pixel.

Hi Lydia (I am assuming, maybe wrongly, that you are Lydia Ng),

Many thanks for your answer. I was particularly interested in the flatenning process that produced the files dorsal_flatmap_paths_100.h5 and top_view_paths_100.h5.

I realized that I forgot to attach to my question this piece of information that I already reported in the github issue. We have now some insight on the process, see the quoted text below, but I was very curious about the implementation details (Which libraries have been used? Is it a volume-based or mesh-based approach? Is the code, or some parts of it, publically available?).

Information on the flattening process reported in https://github.com/AllenInstitute/mouse_connectivity_models/issues/44:

Thanks to a colleague of mine, Sirio Puchet (Blue Brain Project), I have now more insight on this question. Indeed, Sirio pointed out that some details on the flattening process are available in the section Creation of the cortical top-down and flattened views of the CCFv3 for data visualization of Hierarchical organization of cortical and thalamic connectivity (https://www.nature.com/articles/s41586-019-1716-z):

A cortical flatmap was also constructed to enable visualization of anatomical and projection information while preserving spatial context for the entire cortex. The flatmap was created by computing the geodesic distance (the shortest path between two points on a curve surface) between every point on the cortical surface and two pairs of selected anchor points. Each pair of anchor points forms one axis of the 2D embedding of the cortex into a flatmap. The 2D coordinate for each point on the cortical surface is obtained by finding the location such that the radial (circular) distance from the anchor points (in 2D) equals the geodesic distance that was computed in 3D. This procedure produces smooth mapping of the cortical surface onto a 2D plane for visualization. This embedding does not preserve area and the frontal pole and medial-posterior region is highly distorted. As such, all numerical computation is done in 3D space. Similar techniques are used for texture mapping on geometric models in the field of computer [57].

[57] Oliveira, G. N., Torchelsen, R. P., Comba, J. L. D., Walter, M. & Bastos, R. Geotextures: a multi-source geodesic distance field approach for procedural texturing of complex meshes. 2010 23rd SIBGRAPI Conf. Graphics, Patterns and Images 126–133 (IEEE, 2010).