It has been ascertained that the human brain is a complex system studied at multiple scales, from neurons and microcircuits to macronetworks. The brain is characterized by a hierarchical organization that gives rise to its highly topological and functional complexity. Over the last decades, fractal geometry has been shown as a universal tool for the analysis and quantification of the geometric complexity of natural objects, including the brain. The fractal dimension has been identified as a quantitative parameter for the evaluation of the roughness of neural structures, the estimation of time series, and the description of patterns, thus able to discriminate different states of the brain in its entire physiopathological spectrum. Fractal-based computational analyses have been applied to the neurosciences, particularly in the field of clinical neurosciences including neuroimaging and neuroradiology, neurology and neurosurgery, psychiatry and psychology, and neuro-oncology and neuropathology. After a review of the basic concepts of fractal analysis and its main applications to the basic neurosciences in part I of this series, here, we review the main applications of fractals to the clinical neurosciences for a holistic approach towards a fractal geometry model of the brain.

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We study chaotic functions that are exact solutions to nonlinear maps. A generalization of these functions cannot be expressed as a map of type X n+1 = g(X n , X n−1 , . . . , X n−r+1 ).The generalized functions can produce truly random sequences. Even if the initial conditions are known exactly, the next values are in principle unpredictable from the previous values. Although the generating law for these random sequences exists, this law cannot be learned from observations.

A new methodology has been developed for the evaluation and segmentation of brain tumors using information obtained by different magnetic resonance techniques such as in vivo proton magnetic resonance spectroscopy (1HMRS) and relaxometry. In vivo 1HMRS may be used as a preoperative technique that allows noninvasive monitoring of metabolites to identify the different tissue types present in the lesion (active tumor, necrotic tissue, edema, and normal or non-affected tissue). Spatial resolution for treatment consideration may be improved by using 1HMRS combined or fused with images obtained by relaxometry which exhibit excellent spatial resolution. Some segmentation schemes are presented and discussed. The results show that segmentation performed in this way efficiently determines the spatial localization of the tumor both qualitatively and quantitatively. It provides appropriate information for therapy planning and application of therapies such as radiosurgery or radiotherapy and future control of patient evolution.

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