Cortical morphology is notoriously complex and presents unique challenges in anatomic modeling investigations. In response to these challenges, much research has been devoted to developing cortical parameterization and flattening algorithms. These methods optimally transform maps of cortical features onto a simpler, nonconvoluted surface such as a 2D plane [12,26,27,92,126], and an ellipsoid [21,94], or a sphere [23,33,110] (see Fig. 6).
Despite the advantages provided by transformations that simplify its geometry, the cortical surface presents significant challenges for all brain mapping and registration algorithms that strive to match the anatomy of one subject's cortex with another. The need to make comparative measurements at the cortex across subjects requires a surface-to-surface warp that not only matches overall cortical geometry, but also enforces point-to-point correspondence to a higher degree. Specialized approaches have been developed to match cortical regions, so that networks of sulci and gyri are individually matched (Fig. 6; [108,112]). Differences in the serial organization of cortical gyri prevent exact gyrus-by-gyrus matching of one cortex with another. Some cortical areas are particularly subject to variations in the incidence and topology of accessory gyri, and one subject may have two or three gyri where one gyrus is found in another subject. This feature is especially notable in studies of paracingulate and temporo-parietal regions, in particular the planum temporale and posterior perisylvian areas that form a critical part of the language representation of the left hemisphere [59,71,76].
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