A computational method for longitudinal mapping of orientation-specific expansion of cortical surface in infants

The cortical surface of the human brain expands dynamically and regionally heterogeneously during the first postnatal year. As all primary and secondary cortical folds as well as many tertiary cortical folds are well established at term birth, the cortical surface area expansion during this stage is largely driven by the increase of surface area in two orthogonal orientations in the tangent plane: 1) the expansion parallel to the folding orientation (i.e., increasing the lengths of folds) and 2) the expansion perpendicular to the folding orientation (i.e., increasing the depths of folds). This information would help us better understand the mechanisms of cortical development and provide important insights into neurodevelopmental disorders, but still remains largely unknown due to lack of dedicated computational methods. To address this issue, we propose a novel method for longitudinal mapping of orientation-specific expansion of cortical surface area in these two orthogonal orientations during early infancy. First, to derive the two orientation fields perpendicular and parallel to cortical folds, we propose to adaptively and smoothly fuse the gradient field of sulcal depth and also the maximum principal direction field, by leveraging their region-specific reliability. Specifically, we formulate this task as a discrete labeling problem, in which each vertex is assigned to an orientation label, and solve it by graph cuts. Then, based on the computed longitudinal deformation of the cortical surface, we estimate the Jacobian matrix at each vertex by solving a least-squares problem and derive its corresponding stretch tensor. Finally, to obtain the orientation-specific cortical surface expansion, we project the stretch tensor into the two orthogonal orientations separately. We have applied the proposed method to 30 healthy infants, and for the first time we revealed the orientation-specific longitudinal cortical surface expansion maps during the first postnatal year.