Magnetic resonance imaging (MRI) is a way to visualize spatial information about macroscopic ensembles of atomic nuclei, typically the distribution of 1H nuclei within a patient lying in a clinical scanner. Image contrast can be generated in a variety of ways that highlight different properties of these nuclei (e.g., their density, their interaction with electromagnetic fields, their chemical environment, or their diffusion or flow), averaged over small volume elements of the brain, typically with a resolution of 1 cubic mm. Most of the morphometric tools we use and develop were optimized for data obtained by means of T1-weighted MP-RAGE sequences.
The cerebral cortex is a highly folded sheet of gray matter (GM) that lies inside the cerebrospinal fluid (CSF) and surrounds a core of white matter (WM). To analyse cortical structures, it is necessary to remove non-brain tissue and to classify the remaining tissue into GM, WM, and CSF. This early processing step of structural MRI data is called tissue segmentation. A sub-segmentation into the left and right hemisphere and the removal of the brainstem is also necessary.
The tissue segmentation result is used to create a mesh representing the GM sheet. An analogy for the GM sheet is a collapsed balloon. There are two ways to reconstruct it. The first one starts with a fully inflated balloon and changes the surface of the balloon to match the cortical structur (a deformable surface or top-down approach). The second way to reconstruct the surface is based on the tissue map (a bottom-up approach), which tends to produce a more accurate surface reconstruction.
The central surface (CS) of brain cortex may have some analytical advantages compared to boundary surfaces between the gray matter (GM) and either the white matter (WM) or cerebrospinal fluid (CSF). Since the regions between two gyri are often blurred in the segmentation result due to the partial volume effects, it is necessary to reconstruct these regions. We have developed different voxel- and surface-based methods that primarily use distance-based information to reconstruct an accurate CS.
Because we use a bottom-up approach, the reconstructed surface has some topology errors. Noise and partial volume effects lead to mis-classification of brain tissue. These processing errors are visible as bridges between gyri or holes within a gyrus. Because the brain surface has the same shape as a strongly folded balloon, we can remove these defects using topology correction methods.
A common processing step for cortical surfaces is to map the cortical surface mesh to a spherical surface for improved brain registration and advanced analytical techniques. The ideal spherical mapping is isometric — all angles and areas are preserved. Such a mapping potentially improves the quality of subsequent processing steps. However, there is a trade-off between angle and area distortion when mapping the cortical surface to a sphere. Our lab has developed a fast new method to generate a pseudo-isometric spherical mapping of the cortical surface. The initial spherical map is a conformal map produced via the Laplace-Beltrami operator optimized with a Möbius transformation (in figure, LB). The conformal map is then post-processed using a processing pipeline consisting of in-house algorithms designed to reduce area distortion (in figure, Iso). The spherical maps generated using our method have low area and angular distortion.