Three-Dimensional Fractal Analysis of the White Matter Surface from Magnetic Resonance Images of the Human Brain

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Abstract
The convolutions of the cerebral cortex are difficult to describe and delineate. Our understanding of the development of the brain and its associated maldevelopment would be assisted by quantitative analysis of the cortex. Volumetric magnetic resonance (MR) imaging provides high-resolution anatomical data from which we can reconstruct the white matter as a three-dimensional object and extract its surface (the grey/white matter interface). Three-dimensional fractal analysis of this surface is a method of quantifying the surface complexity dependent upon the variation of the surface area under different scales of inspection. We estimate the fractal dimension of the white matter surface for each hemisphere and 10 coronal blocks of each hemisphere in 30 normal adult subjects. These values are tightly distributed and have been used to define a normal range of fractal dimensions. Abnormal fractal dimensions were found in 8/16 subjects with epilepsy and a gyral abnormality observed on routine MR imaging; and in 9/23 subjects with epilepsy and normal routine MR imaging. These analytical techniques offer additional information about the structure of the cortex in normal brains and about abnormalities of structure in subjects with suspected but unobserved structural abnormalites.