# Architectonics-informed partition of the cortex at sub-millimetre resolution

Yann Leprince, Clara Fischer, Jean-François Mangin, Benoît Larrat, Sébastien Mériaux, Cyril Poupon, Isabel Reillo, Victor Borrell, Ophélie Foubet, Roberto Toro, et al.

<figure><img src="image_1.png" /></figure>

## To cite this version:

Yann Leprince, Clara Fischer, Jean-François Mangin, Benoît Larrat, Sébastien Mériaux, et al. Architectonics-informed partition of the cortex at sub-millimetre resolution. 20th Annual Meeting of the Organization for Human Brain Mapping (OHBM), Jun 2014, Hamburg, Germany. , 5, pp.951, 2014, F1000Posters. cea-01074735

HAL Id: cea-01074735

https://cea.hal.science/cea-01074735

Submitted on 15 Oct 2014

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<figure><img src="image_2.png" /></figure>
# Architectonics-informed partition of the cortex at sub-millimetre resolution

Yann Leprince¹,², Clara Fischer¹,³, Jean-François Mangin¹,³, Benoît Larrat¹, Sébastien Mériaux¹, Cyril Poupon¹,³, Isabel Reillo⁴, Victor Borrell⁴, Ophélie Foubet⁵, Roberto Toro⁵, Denis Rivière¹,³

¹NeuroSpin, CEA Saclay, France
²Université Paris-Sud 11, Orsay, France
³CATI Multicenter Neuroimaging Platform

NeuroSpin

cea

UNIVERSITÉ
PARIS
SUD

CATI

⁴Instituto de Neurociencias, Alicante, Spain
⁵Institut Pasteur, Paris, France

Corresponding author: yann.leprince@ylep.fr

#3560 (OHBM 2014, Hamburg, 11. June 2014)

<figure><img src="image_3.png" /></figure>

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.
To view a copy of this license, visit http://creativecommons.org/licenses/by-sa/4.0/.

## Overview

We propose a method to partition the cortex into cortical traverses, in the geometry of the original image. Two properties make this a good basis for studying cortical lamination:

- each region contains samples from the whole cortical thickness;

- each voxel appears in one, and only one traverse.

<figure><img src="image_4.png" /><figcaption>pial interface</figcaption></figure>

Cortical columns and layers are visible on this Nissl-stained histological slice of a baboon brain (courtesy of Thierry Delzescaux)

# 1 Preparing the data

<figure><img src="image_5.png" /></figure>

Starting point of the method:
voxel-wise segmentation in
**grey, white**, and **CSF**
compartments.

Built from the image below
using an adapted Morphologist
segmentation pipeline
[www.brainvisa.info].

<figure><img src="image_6.png" /></figure>

Test data set:

- post-mortem ferret brain

- 7 T small animal scanner

- quantitative T2 map

- 0.12 mm isotropic resolution

- whole brain 3D image

# 2 Modelling cortical columns

Cortical columns cannot be directly imaged with MRI. Previous evidence [Schleicher et al. 2005] suggests that the direction of cortical columns is well represented by the gradient of a Laplacian field, as introduced by [Jones et al. 2000].

The Laplacian field is defined by solving the Laplace equation $\Delta T=0$ within grey matter, by imposing $T=1$ in the white matter and $T=0$ in the CSF. Grey levels represent $T$, green arrows represent the direction of its gradient $\nabla T$.

The results are shown on a single slice, but all steps of the algorithm work on volume images to utilize full 3D geometric information.

<figure><img src="image_7.png" /></figure>

# 3 Labelling the interfaces

<figure><img src="image_8.png" /><figcaption>2D slice of the
real 3D result</figcaption></figure>

<figure><img src="image_9.png" /></figure>

Each voxel of the
grey-white and grey-CSF
interfaces is assigned a
unique label.

# 4 Grouping interface voxels

<figure><img src="image_10.png" /></figure>

Each interface voxel is advected towards the other interface along $\nabla T$ towards the grey-white boundary. The label of the voxel reached is assigned to the voxel at the origin of the advection.

As a result, interface
voxels are grouped
at the exterior of
curved regions.

<figure><img src="image_11.png" /><figcaption>2D slice of the
real 3D result</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>2D slice of the
real 3D result</figcaption></figure>

# 6 Merging regions

The regions are aggregated using an iterative merging algorithm, in order to reduce “over-parcellation” and obtain regions of a defined, configurable size.

The merging is based on the quality factor $Q$ of the regions, which is defined as $V / (S_{pial} + S_{white})$, with $V$ the volume of the region, and $S_x$ the approximate surface projection of the region onto each interface, estimated by fitting an ellipsoid to the ends of the advection paths.

Resulting regions are dense and traverse the whole cortical thickness.

<figure><img src="image_13.png" /><figcaption>Region volume (mm³)</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Region volume (mm³)</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>pial interface</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>grey-white interface</figcaption></figure>

# 5 Grouping cortical voxels

Each cortical voxel is advected towards both interfaces along $\nabla T$. The labels at the end of these paths form a pair ($L_{white}$, $L_{pial}$). Cortical voxels associated with a same pair of labels are grouped together.

The resulting regions are aligned along the Laplacian field, but many of them are too small and do not traverse the whole cortical thickness.

<figure><img src="image_17.png" /><figcaption>2D slice of the
real 3D result</figcaption></figure>

<figure><img src="image_18.png" /></figure>

## Perspective: cortical lamination analysis

Each region created by this method, when associated with a voxel-wise measurement of depth, can be used to characterize the evolution of signal intensity along cortical thickness.

This yields lamination profiles that reflect the local cytoarchitecture of the cortex.

The regions could be used as building blocks of a cortical parcellation based on the extracted cytoarchitectural data.

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

S. E. Jones, B. R. Buchbinder and I. Aharon. Three-dimensional mapping of cortical thickness using Laplace's Equation. Human Brain Mapping 11, 12–32 (2000).
A. Schleicher et al. Quantitative architectural analysis: a new approach to cortical mapping. Anat Embryol 210, 373–386 (2005).