Is the brain cortex a fractal?

Abstract

The notion of fractal has been largely used to describe geometrical properties of complex objects in biology and medicine. In the present study the question is addressed whether the human cerebral cortex is self-similar in a statistical sense, which is commonly referred to as being a fractal. A new calculational method is presented, which is volumetric and based on the fast Fourier transform (FFT) of segmented three-dimensional high-resolution magnetic resonance images. The analysis covers a wide range of spatial scales from the size of the whole cortex to the ultimate pixel size. Results obtained in six subjects confirm the fractal nature of the human cerebral cortex down to a spatial scale of 3 mm. The obtained fractal dimension is D = 2.80 +/- 0.05, which is in reasonable agreement with previously reported results. Deployment of FFT enables a simple interpretation of the results and yields a high performance, which is necessary to analyze the entire cortex. Thus the FFT-based analysis of segmented MR images offers a comprehensive approach to study neurodevelopmental and neurodegenerative changes in the fractal geometry of the cerebral cortex.