Fractal Analysis of White Matter of The Human Cerebellum Hemispheres

Morphological investigations of cerebellar lobules are usually performed using standard methods of morphometry such as: measurement of volumes of the gray and white matters of the cerebellar lobules, which determine linear dimensions of the cerebellum. Fractal analysis is used for morphometric study of complex objects with properties of fractals such as self-similarity and scale invariance. The aim of the paper is to study the fractal dimension of white matter of the human cerebellar hemispheric lobules I-IX on serial parasagittal sections. Research was conducted in Kharkiv regional bureau of forensic medicine. The study involved 100 cerebella of people of both sexes who died without causes with pathology of brain who were 20-95 years old. Parasagittal sections of the human cerebellar hemispheres were investigated. Fractal analysis was conducted using the original box-counting method. Fractal index of white matter of the cerebellar hemispheric lobules varies from 1.202 to 1.629. The highest fractal index was found in hemispheric lobules VI-VII that are associated with neocerebellar vermal lobules. The lowest fractal index was found in cerebellar tonsils (lobule IX). The average fractal dimension of the lobules I-V was indicated as 1.341±0.014 (1.339±0.021 in the left hemisphere, and 1.342±0.020 in the right hemisphere correspondingly). The average fractal dimension of the lobule VI is 1.452±0.023 (1.435±0.033 was in the left hemisphere, 1.468±0.032 was in the right hemisphere). The average fractal dimension of the lobule VII Af is 1.395±0.014 (1.392±0.019 in the left hemisphere, 1.397±0.019 - in the right hemisphere). The average fractal dimension of the lobules VII At and VII B is 1.327±0.017 (1.328±0.024 in the left hemisphere, 1.326±0.024 in the right hemisphere). The average fractal dimension of the lobule VIII is 1.311±0.014 (1.314±0.020 in the left hemisphere, 1.308±0.020 in the right hemisphere). The average fractal dimension of the lobule IX is 1.215±0.008 (1.212±0.012 in the left hemisphere, 1.217±0.011 in the right hemisphere). Interhemispheric difference of fractal index of the particles varies from 0.016% to 4.92%. Fractal index of the lobules I-VI, VIIAt, VIII and IX decreases in the lateral cerebellar hemispheres areas; fractal index of the lobule VIIAf is the lowest in paravermal areas and increases in media-lateral direction. Peculiarities of the structure of the cerebellar lobules and difference of the fractal index are associated with scale invariance and patterns of spatial organization of the quasi-fractal structures. The increase of the structure size (scale) increases the complexity of its organization. The fractal analysis can be used as an objective morphometric criterion for the diagnosis of various diseases of the cerebellum and other structures of the central nervous system.