Fractal dimension analysis of the cortical ribbon in mild Alzheimer's disease

Fractal analysis methods are used to quantify the complexity of the human cerebral cortex. Many recent studies have focused on high resolution three-dimensional reconstructions of either the outer (pial) surface of the brain or the junction between the gray and white matter, but ignore the structure between these surfaces. This study uses a new method to incorporate the entire cortical thickness. Data were obtained from the Alzheimer's Disease (AD) Neuroimaging Initiative database (Control N=35, Mild AD N=35). Image segmentation was performed using a semi-automated analysis program. The fractal dimension of three cortical models (the pial surface, gray/white surface and entire cortical ribbon) were calculated using a custom cube-counting triangle-intersection algorithm. The fractal dimension of the cortical ribbon showed highly significant differences between control and AD subjects (p<0.001). The inner surface analysis also found smaller but significant differences (p<0.05). The pial surface dimensionality was not significantly different between the two groups. All three models had a significant positive correlation with the cortical gyrification index (r>0.55, p<0.001). Only the cortical ribbon had a significant correlation with cortical thickness (r=0.832, p<0.001) and the Alzheimer's Disease Assessment Scale cognitive battery (r=-0.513, p=0.002). The cortical ribbon dimensionality showed a larger effect size (d=1.12) in separating control and mild AD subjects than cortical thickness (d=1.01) or gyrification index (d=0.84). The methodological change shown in this paper may allow for further clinical application of cortical fractal dimension as a biomarker for structural changes that accrue with neurodegenerative diseases.