Fractal analysis of images in medicine and morphology: basic principles and methodologies

Background. Fractal analysis is an informative and objective method of mathematical analysis that can complement existing methods of morphometry and provides a comprehensive quantitative assessment of the spatial configuration of irregular anatomical structures. Objective: a comparative analysis of fractal analysis methods used for morphometry in biomedical research. Methods. A comprehensive analysis of morphological studies, based on fractal analysis. Results. Different types of medical images with different preprocessing algorithms can be used for fractal analysis. The parameter determined by fractal analysis is the fractal dimension, which is a measure of the complexity of the spatial configuration and the degree of filling of space with a certain geometric object. The most known methods of fractal analysis are the following: box counting, caliper, pixel dilation, "mass-radius", cumulative intersection, grid intercept. The box counting method and its modifications is the most commonly used method due to the simplicity and versatility. Different methods of fractal analysis have a similar principle: fractal measures (different geometric figures) of a certain size completely cover the structure in the image, size of fractal measure is iteratively changed, and the minimum number of fractal measures covering the structure is calculated. Methods of fractal analysis differ in the type of fractal measure, which can be a linear segment, a square of a fractal grid, a cube, a circle, a sphere etc. Conclusion. The choice of the method of fractal analysis and image preprocessing method depends on the studied structure, features of its spatial configuration, the type of image used for the analysis, and the aim of the study.

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.