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Surface based Analysis
- Cortex analysis
- Deep brain analysis
- Functional data analysis
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Cortex analysis Deep brain analysis Functional data analysis
Cortical analysis using surface-based methods
Traditionally, in the analyses of human brain structure, region of interest (ROI) methods have been used to suggest volumetric changes and differences within/between groups. Manually segmented ROI-based analyses are intensive labor and suffer from the issues of intra- and interrater reliability issues and different ROI definitions. Voxel-based morphometry (VBM) is an observer-independent automatic methodology that is implemented across the cortex. However, this method also exhibits limited accuracy in the measurement of cortical morphology, especially in brain regions where fine anatomic details are often obscured by a partial volume effect. The concepts of gray matter density in VBM are central to the interpretation of the results of group data. Recently, to reflect more accurate cortical geometry and overcome partial volume effect, the analyses using cortical surface model have been performed. Cortical surface-based analysis can make it possible to measure cortical thickness in millimeters (more precise measurement in deep sulci as a cortical sheet). In addition, cortical shape and folding pattern can be analyzed, which is not possible in volumetric methods.

Cortical surface extraction
The native MR images are processed through the anatomical pipeline. The surfaces of the inner and outer cortex were automatically fitted using the Constrained Laplacian-Based Automated Segmentation with Proximities algorithm (Kim et al., 2005, NeuroImage) that is sort of deformable model algorithm. The reconstructed hemispheric cortical surfaces consisted of 81,920 high-resolution meshes of discrete triangular elements.

Various measurements for cortical structure analysis

Cortical thickness
The inner and outer surfaces had the same number of vertices, and there was a close correspondence between the counterpart vertices of the inner and outer cortical surfaces. The cortical thickness was defined as the Euclidean distance between these linked vertices.

Surface-based diffusion smoothing and 2-D spherical surface registration are performed to vertex-by-vertex analysis.

Our application study
- Gender difference in cortical thickness (Im et al., 2006, NeuroImage)

- Cortical thickness in MCI (Seo et al., 2007, NeuroImage)

Cortical surface area
Cortical surface area is calculated, which is the straightforward sum of the areas of the triangles making up the surface model. Cortical surface area can be used to suggest the overall degree of folding.

Sulcal depth
Previous studies have reported that the change of sulcal depth is associated with brain disease. Sulcal depth maps are generated by measuring the 3-D Euclidean distance from each vertex in the cortical surface to the nearest voxel on a cerebral hull volume. The Euclidean distance as the measure of sulcal depth was used in previous studies and one of them showed cortical folding abnormalities in Williams Syndrome.

Cortical convolution (mean curvature)
In order to quantify the degree of sharpness and convolution of cortical folding regardless of cortical depth, mean curvature was computed at the vertices that lie within the cortical surface.

Mean curvature on sulcal walls is measured to estimates the degree of sulcal convolution regardless of the effect of sulcal fundic sharpness in order to differentiate between these scenarios for more definite interpretation. Areas of sulcal wall are defined using the sulcal depth map as lying between specific depths.

Fractal dimension
Fractal dimension (FD) provides a quantitative description of the structural complexity in the cerebral cortex. After extracting 3D vertex information of cortical surface, FD is measured using box-counting method.

Our previous study (Im et al, 2006, Hum. Brain Mapp.)
FD is an extremely compact measure of shape complexity, condensing all details into a single numeric value. We interpreted the variation of the FD in the cortical surface of normal controls through multiple regression analysis with cortical thickness, sulcal depth and folding area, related to cortical complexity. Human cortex develops a complex structure through the thinning of cortical thickness and by increasing the frequency of folds and the convolution of gyral shape rather than by deepening sulcal regions.

Folding area
Folding area calculates the area of the folded regions normalized by whole surface area in the outer smoothed cortical surface model. The purpose is to detect how large area the folding regions occupy in entire surface area. The folding regions are defined using mean curvature in the 3-D triangular surface model.

Our Application study using folding area and mean curvature
(Im et al., 2007 in OHBM conference)

The purpose is to analyze the pattern of cortical folding in MCI and AD. Using the combination of folding area and mean curvature, the results suggest that sulcal widening becomes more severe across the entire cortex in AD than in old normal and MCI groups.