Local cortical surface complexity maps from spherical harmonic reconstructions

Altered cortical surface complexity and gyrification differences may be a potentially sensitive marker for several neurodevelopmental disorders. We propose to use spherical harmonic (SPH) constructions to measure cortical surface folding complexity. First, we demonstrate that the complexity measure is accurate, by applying our SPH approach and the more traditional box-counting method to von Koch fractal surfaces with known fractal dimension (FD) values. The SPH approach is then applied to study complexity differences between 87 patients with DSM-IV schizophrenia (with stable psychopathology and treated with antipsychotic medication; 48 male/39 female; mean age = 35.5 years, SD = 11.0) and 108 matched healthy controls (68 male/40 female; mean age = 32.1 years, SD = 10.0). The global FD for the right hemisphere in the schizophrenia group was significantly reduced. Regionally, reduced complexity was also found in temporal, frontal, and cingulate regions in the right hemisphere, and temporal and prefrontal regions in the left hemisphere. These results are discussed in terms of previously published findings. Finally, the anatomical implications of a reduced FD are highlighted through comparison of two subjects with vastly different complexity maps.