Local Spectral Analysis of the Cerebral Cortex: New Gyrification Indices

Gyrification index (GI) is an appropriate measure to quantify the complexity of the cerebral cortex. There is, however, no universal agreement on the notion of surface complexity and there are various methods in literature that evaluate different aspects of cortical folding. In this paper, we give two intuitive interpretations on folding quantification based on the magnitude and variation of the mean curvature of the cortical surface. We then present a local spectral analysis of the mean curvature to introduce two local gyrification indices that satisfy our interpretations. For this purpose, the graph windowed Fourier transform is extended to the framework of surfaces discretized with triangular meshes. An adaptive window function is also proposed to deal with the intersubject cortical size variability. The intrinsic nature of the method allows us to compute the degree of folding at different spatial scales. Our experiments show that while more classical surface area-based GIs may fail at differentiating deep folds from very convoluted ones, our spectral GIs overcome this issue. The method is applied to the cortical surfaces of 124 healthy adult subjects of OASIS database and average gyrification maps are computed and compared with other GI definitions. In order to illustrate the capacity of our method to capture and quantify important aspects of gyrification, we study the relationship between brain volume and cortical complexity, and design a scaling analysis with a power law model. Results indicate an allometric relation and confirm the well-known observations that larger brains are more folded. We also perform the scaling analysis at the vertex level to investigate how the degree of folding varies locally with the brain volume. Results reveal that in our healthy adult brain database, cortical regions which are the least folded on average show an increased folding complexity when brain size increases.