Fractal Complexity of the Human Cortex Is Increased in Williams Syndrome

We developed a new algorithm to measure the fractal dimension, or complexity, of the human cerebral cortex. Cortical complexity was found to be significantly increased in Williams syndrome, a genetic condition associated with deletion of ~20 contiguous genes on chromosome 7 [cf. 1,2]. Most prior complexity measures such as the gyrification index [2,3] typically measure the cortical contour in a specific image slice. By contrast, the proposed fractal dimension takes into account the full 3D cortical surface geometry, and is independent of brain scale, orientation and the direction of image acquisition.