FRACTAL DIMENSION IN MORPHOLOGY AND MEDICINE: THEORETICAL BASES AND PRACTICAL APPLICATION: review

Abstract

Morphometry is an integral part of most modern morphological studies and the classic morphological morphometric methods and techniques are often borrowed for research in other fields of medicine. The majority of morphometric techniques are derived from Euclidean geometry. In the past decades, the principles, parameters and methods of fractal geometry are increasingly used in morphological studies. The basic parameter of fractal geometry is fractal dimension. Fractal dimension allows you to quantify the degree of filling of space with a certain geometric object and to characterize the complexity of its spatial configuration. There are many anatomical structures with complex irregular shapes that cannot be unambiguously and comprehensively characterized by methods and techniques of traditional geometry and traditional morphometry: irregular linear structures, irregular surfaces of various structures and pathological foci, structures with complex branched, tree-like, reticulated, cellular or porous structure, etc. Fractal dimension is a useful and informative morphometric parameter that can complement existing quantitative parameters to quantify objective characteristics of various anatomical structures and pathological foci. Fractal analysis can qualitatively complement existing morphometric methods and techniques and allow a comprehensive assessment of the spatial configuration complexity degree of irregular anatomical structures. The review describes the basic principles of Euclidean and fractal geometry and their application in morphology and medicine, importance and application of sizes and their derivatives, topological, metric and fractal dimensions, regular and irregular figures in morphology, and practical application of fractal dimension and fractal analysis in the morphological studies and clinical practice.