Computation of Local Fractal Dimension Values of the Human Cerebral Cortex

Abstract

Objectives:\rThe purpose of this paper is to describe a technique for computing the local\rfractal dimension of the human cerebral cortex as extracted from\rhigh-resolution magnetic resonance imaging scans. Methods: 3D models of the\rhuman cerebral cortex were extracted from high resolution magnetic resonance\rimages of 10 healthy adult volunteers using FreeSurfer. The local fractal dimension of the cortex was computed using a custom-written\rcube-counting algorithm. The effect of constraining the maximum region size on\rthe measured value of local fractal dimension was examined. A proof of\rprinciple was demonstrated by comparing an individual with Alzheimer’s disease\rto a healthy individual. Results: Local values of cortical fractal dimension\rcan be obtained by constraining the size of the region over which the cube\rcounting is performed. Cubic regions of intermediate size (30 × 30 × 30 mm)\ryielded a profile that demonstrated greater regional variability compared to\rsmaller (15 × 15 × 15 mm) or larger (60 × 60 × 60 mm) region sizes. Conclusions:\rLocal fractal dimension of the cerebral cortex is a novel measure that may\ryield additional, quantitative insight into the clinical meaning of cortical\rshape changes.