3D Normal Coordinate Systems for Cortical Areas

TL;DR

This paper introduces a diffeomorphic algorithm to generate 3D coordinate grids in the cortical ribbon, enabling precise cortical morphometry by modeling orthogonal columns between inner and outer surfaces.

Contribution

It presents a novel surface-based diffeomorphic method to create normal coordinate systems in the cortex, facilitating accurate measurement of cortical thickness and structure.

Findings

Effective in modeling cortical columns as orthogonal to surfaces

Applied successfully to auditory cortices in humans and cats

Potential for advanced cortical morphometry studies

Abstract

A surface-based diffeomorphic algorithm to generate 3D coordinate grids in the cortical ribbon is described. In the grid, normal coordinate lines are generated by the diffeomorphic evolution from the grey/white (inner) surface to the grey/csf (outer) surface. Specifically, the cortical ribbon is described by two triangulated surfaces with open boundaries. Conceptually, the inner surface sits on top of the white matter structure and the outer on top of the gray matter. It is assumed that the cortical ribbon consists of cortical columns which are orthogonal to the white matter surface. This might be viewed as a consequence of the development of the columns in the embryo. It is also assumed that the columns are orthogonal to the outer surface so that the resultant vector field is orthogonal to the evolving surface. Then the distance of the normal lines from the vector field such that the inner surface evolves diffeomorphically towards the outer one can be construed as a measure of thickness. Applications are described for the auditory cortices in human adults and cats with normal hearing or hearing loss. The approach offers great potential for cortical morphometry.