How to measure cortical folding from MR images: a step-by-step tutorial to compute local gyrification index

Cortical folding (gyrification) is determined during the first months of life, so that adverse events occurring during this period leave traces that will be identifiable at any age. As recently reviewed by Mangin and colleagues(2), several methods exist to quantify different characteristics of gyrification. For instance, sulcal morphometry can be used to measure shape descriptors such as the depth, length or indices of inter-hemispheric asymmetry(3). These geometrical properties have the advantage of being easy to interpret. However, sulcal morphometry tightly relies on the accurate identification of a given set of sulci and hence provides a fragmented description of gyrification. A more fine-grained quantification of gyrification can be achieved with curvature-based measurements, where smoothed absolute mean curvature is typically computed at thousands of points over the cortical surface(4). The curvature is however not straightforward to comprehend, as it remains unclear if there is any direct relationship between the curvedness and a biologically meaningful correlate such as cortical volume or surface. To address the diverse issues raised by the measurement of cortical folding, we previously developed an algorithm to quantify local gyrification with an exquisite spatial resolution and of simple interpretation. Our method is inspired of the Gyrification Index(5), a method originally used in comparative neuroanatomy to evaluate the cortical folding differences across species. In our implementation, which we name local Gyrification Index (lGI(1)), we measure the amount of cortex buried within the sulcal folds as compared with the amount of visible cortex in circular regions of interest. Given that the cortex grows primarily through radial expansion(6), our method was specifically designed to identify early defects of cortical development. In this article, we detail the computation of local Gyrification Index, which is now freely distributed as a part of the FreeSurfer Software (http://surfer.nmr.mgh.harvard.edu/, Martinos Center for Biomedical Imaging, Massachusetts General Hospital). FreeSurfer provides a set of automated reconstruction tools of the brain's cortical surface from structural MRI data. The cortical surface extracted in the native space of the images with sub-millimeter accuracy is then further used for the creation of an outer surface, which will serve as a basis for the lGI calculation. A circular region of interest is then delineated on the outer surface, and its corresponding region of interest on the cortical surface is identified using a matching algorithm as described in our validation study(1). This process is repeatedly iterated with largely overlapping regions of interest, resulting in cortical maps of gyrification for subsequent statistical comparisons (Fig. 1). Of note, another measurement of local gyrification with a similar inspiration was proposed by Toro and colleagues(7), where the folding index at each point is computed as the ratio of the cortical area contained in a sphere divided by the area of a disc with the same radius. The two implementations differ in that the one by Toro et al. is based on Euclidian distances and thus considers discontinuous patches of cortical area, whereas ours uses a strict geodesic algorithm and include only the continuous patch of cortical area opening at the brain surface in a circular region of interest.