Methods and Application in Fractal Analysis of Neuroimaging Data

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Background

The high complexity of the human brain inherently underpins the incredible variety of cognitive, motor, and sensory functions. Measuring such complexity may help define a comprehensive feature able to represent the general organization of the brain. Fractal analysis is a framework able to represent highly complex structures or signals and gives complementary and powerful tools for capturing and quantifying brain complexity.

A fractal object has a property of self-similarity. It can be subdivided into parts, each of which (at least approximately) is a reduced-size copy of the whole. A strict self-similarity exists only in objects defined by mathematical formulas. On the contrary, real-world, natural, or computer-simulated fractals are self-similar only in a statistical sense and over a limited interval of spatial scales, i.e., they show the same statistical distribution of space-filling over some scales of observation. In the last few years, fractal analysis has been applied to many structures in the brain, including the cerebral cortex and subcortical white matter, mainly using T1- and diffusion-weighted MRI data. Although fractality is generally perceived in two dimensions also, a time series (i.e. unidimensional data) might shows self-similarity properties. Such signals are said to be scale-invariant or scale-free because the pattern is much the same regardless of the scale used. The relationship between the change in timescale and the change in amplitude scale often follows a power relationship. Human neurophysiological processes are characterized by a high degree of variability in the time domain (non-stationarity) and randomness that could be attributed to the interaction of internal and external factors influencing the organism. In recent years, fractal analysis has been successfully applied to EEG and haemodynamic signals, providing a measure of predictability and regularity across different areas of neuroscience, such as consciousness research, mood and anxiety disorders, schizophrenia, neurodevelopmental and neurodegenerative disorders, as well as physiological changes across the lifespan.

In this Research Topic, we offer an overview of the current and potential methods and applications of fractal geometry to analyze structural and functional neuroimaging data. We accept reviews, original research, and perspective articles to create new insights concerning the quantification of the structural and functional complexity of neuroimaging data and shape novel research applications.

Keywords: Fractal Analysis, Neuroimaging, Neuroradiology, Brain, EEG, fractal dimension, functional complexity, MRI, neuroimaging data, self-similarity, structural complexity.

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