Estimating the Complexity of the Cerebral Cortex Folding with a Local Shape Spectral Analysis

Abstract

The human cerebral cortex is a highly folded structure that can be modeled by a surface extracted in vivo from magnetic resonance imaging data. The folding complexity of this surface has been shown to be a relevant biological measurement, often estimated locally and referred to by the term “gyrification index” (GI). There is, however, no universal agreement on the notion of surface complexity and various methods have been presented that evaluate different aspects of cortical folding. In this chapter, we show how a local spectral analysis of the cortical surface mean curvature can address this problem and provide two well-defined gyrification indices. Specifically, we extended the concept of graph windowed Fourier transform to the framework of surfaces modeled by triangular meshes. The intrinsic nature of the method allows us to compute the folding complexity at different spatial scales. We show that our approach overcomes a major flaw in other more classical GI estimators, namely the impossibility to differentiate deep cortical folds from shallower but more oscillating ones. We applied our method on synthetic data as well as on a database of 124 healthy adult subjects and showed that it verifies important properties and capture important aspects of cortical gyrification. A comparison with other GI definitions is also provided.