TITLE:
Computation of Local Fractal Dimension Values of the Human Cerebral Cortex
AUTHORS:
Richard D. King
KEYWORDS:
Fractal, Dimension, Cortex, Imaging Biomarkers, Local
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.12,
June
26,
2014
ABSTRACT: Objectives:
The purpose of this paper is to describe a technique for computing the local
fractal dimension of the human cerebral cortex as extracted from
high-resolution magnetic resonance imaging scans. Methods: 3D models of the
human cerebral cortex were extracted from high resolution magnetic resonance
images of 10 healthy adult volunteers using FreeSurfer. The local fractal dimension of the cortex was computed using a custom-written
cube-counting algorithm. The effect of constraining the maximum region size on
the measured value of local fractal dimension was examined. A proof of
principle was demonstrated by comparing an individual with Alzheimer’s disease
to a healthy individual. Results: Local values of cortical fractal dimension
can be obtained by constraining the size of the region over which the cube
counting is performed. Cubic regions of intermediate size (30 × 30 × 30 mm)
yielded a profile that demonstrated greater regional variability compared to
smaller (15 × 15 × 15 mm) or larger (60 × 60 × 60 mm) region sizes. Conclusions:
Local fractal dimension of the cerebral cortex is a novel measure that may
yield additional, quantitative insight into the clinical meaning of cortical
shape changes.