Measures of folding applied to the development of the human fetal brain

Abstract

Previous work has suggested the existence of differences between the cerebral cortex of normal individuals, and those of patients with diseases such as epilepsy and schizophrenia. These shape abnormalities may be of developmental origin. Improved shape measures could provide useful tools for neuroscience research and patient diagnosis. We consider the theoretically desirable properties of measures of brain shape. We have implemented seven measures, three from the neuroscience literature, and four new to this field. Three of the measures are zero-order and four are second-order with respect to the surface. We validate the measures using simple geometrical shapes, and a collection of magnetic resonance scans of ten histologically normal ex vivo fetal brains with gestational ages from 19-42 weeks. We then apply the measures to MR scans from two histologically abnormal ex vivo brains. We demonstrate that our implementation of the measures is sensitive to anatomical variability rather than to the discreteness of the image data. All the measures were sensitive to changes in shape during fetal development. Several of the measures could distinguish between the normal and abnormal fetal brains. We propose a multivariate approach to studying the shape of the cerebral cortex, in which both zero-order and second-order measures are used to quantify folding.

Gender Differences in Cerebral Cortical Folding: Multivariate Complexity-Shape Analysis with Insights into Handling Brain-Volume Differences

“…A second class of measures, including IPR, ICI, MCN, GCN, and AC [6,11,12,8] (all normalized by surface-patch area or, equivalently, ICV 2/3 ), is designed to be invariant to scale. However, this sacrifices invariance to replication.…”

“…Furthermore, the phenomenon of cortical folding has an inherent large-scale or non-local character. A second class of approaches propose region-based folding descriptors [5,6,7], which avoid the challenges associated with normalization by reducing spatial sensitivity from a voxel to a region of interest (ROI) that can be reliably defined in each individual based on observed homologous features.…”

“…Gyrification index (GI) [13] is the ratio of the lengths of a planar curve to its envelope. Convexity ratio (CR) [6] is the ratio of the area of the surface to the area of the convex hull/envelope of the surface. IPR [6,11,12] is the ratio of the surface area to the two-third power of the volume enclosed by the surface.…”

“…Convexity ratio (CR) [6] is the ratio of the area of the surface to the area of the convex hull/envelope of the surface. IPR [6,11,12] is the ratio of the surface area to the two-third power of the volume enclosed by the surface. Average curvedness (AC) [8] measures the deviation of the surface from a plane.…”

“…intrinsic curvature index (ICI) [5] sums up degrees of hemisphericity, mean curvature norm (MCN) [6] sums up degrees of hemisphericity and cylindricity, Gaussian curvature norm (GCN) [6] sums up degrees of hemisphericity and saddle-likeness, average shape index (AS) [8] sums up shape measures, etc.…”