Quantifying Gyrification Using Laplace Beltrami Eigenfunction Level-Sets

Cortical surface is folded into gyri and sulci in the brains of higher mammals. Gyrification indices (GI) are widely used to characterise cortical folding complexity, and are important metrics employed in the quantitative assessment of normal brain development and neurodevelopmental disorders. A new GI metric is proposed that endeavours to combine the advantages of surface-based methods with curvature-based methods. The proposed metric employs a measurement of curvature; however, the use of Laplace-Beltrami eigen-function level-sets introduces the advantage of focusing on folds, a characteristic previously attributed only to surface-based methods. Applying Laplace-Beltrami eigenfunction level-sets also avoids the need to define an outer surface and correspondence function required by surface-based methods. We demonstrate the utility of the proposed GI with an application to fetal ovine MRI data across key developmental time points.