Abstract
The cerebral cortex manifests an inherent structural complexity of folding. The fractal geometry describes the complexity of structures which show self-similarity in a proper interval of spatial scales. In this study, we aimed at evaluating in-vivo the effect of different criteria for selecting the interval of spatial scales in the estimation of the fractal dimension (FD) of the cerebral cortex in T1-weighted magnetic resonance imaging (MRI). We compared four different strategies, including two a priori selections of the interval of spatial scales, an automated selection of the spatial scales within which the cerebral cortex manifests the highest statistical self-similarity, and an improved approach, based on the search of the interval of spatial scales which presents the highest rounded R2adj coefficient and, in case of equal rounded R2adj coefficient, preferring the widest interval in the log–log plot. We employed two public and international datasets of in-vivo MRI scans for a total of 159 healthy subjects (age range 6–85 years). The improved approach showed strong associations of FD with age and yielded the most accurate machine learning models for individual age prediction in both datasets. Our results indicate that the selection of the interval of spatial scales of the cerebral cortex is thus critical in the estimation of FD.
Highlights
IntroductionThe fractal geometry describes the complexity of structures which show self-similarity in a proper interval of spatial scales
The cerebral cortex manifests an inherent structural complexity of folding
We estimated the fractal dimension (FD) of the cerebral cortex of each subject using our implementation of the 3-D box counting algorithm[29, 30] and four different strategies for the selection of spatial scales
Summary
The fractal geometry describes the complexity of structures which show self-similarity in a proper interval of spatial scales. We aimed at evaluating in-vivo the effect of different criteria for selecting the interval of spatial scales in the estimation of the fractal dimension (FD) of the cerebral cortex in T1-weighted magnetic resonance imaging (MRI). Using T1-weighted MRI, fractal properties have been demonstrated in grey matter (GM) and WM surfaces and segmentations (see, e.g.,5, 13–17) In this regard, Hofman was one of the first researchers who has shown that the cerebral cortex manifests fractality[16], and this property was confirmed by other studies, including the works by Free et al and Kiselev et al who demonstrated, using different approaches, that the cerebral cortex presents. The fractal analysis has been effectively applied to time series of brain signals, e.g., in functional M RI18–20
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