Cluster Analysis of Human Cerebellum Fractal Dimension

Abstract

The cerebellum is a multifractal that includes several fractal clusters that correspond to different components of the cerebellar tissue: white matter and layers of the cortex. A fractal analysis (pixel dilation method in one of the author's modifications) was used to determine the complexity of spatial organization and the degree of filling of space with different components of cerebellar tissue. The purpose of the study was to determine clusters of fractal dimension of various components of human cerebellar tissue according to magnetic resonance imaging. Material and methods. The study was performed on digital T2 weighted images of magnetic resonance images of 30 patients (15 men and 15 women) who did not have pathological changes of the brain. Fractal analysis was performed using the pixel dilation method. The fractal dimension of cerebellar tissue for its components in the range of brightness values from 0 to 255 was determined. The difference in fractal dimension increase at different parts of the brightness range was calculated. Results and discussion. The study showed that the increase in fractal dimension is not gradual and has four zones of the most pronounced increase in values: 70-80, 85-90, 95-105 and 110-120. These areas can be separated into distinct clusters that correspond to the main components of the cerebellar tissue. The first cluster with the most intense increase of fractal dimension corresponds to the white matter of the cerebellum, which has the biggest density and the lowest values of brightness, the second – the granular layer of the cortex, the third – the molecular layer of the cortex. The fourth, least pronounced cluster corresponds to the pixels of the image with the highest brightness level, which correspond to the meninges. Conclusion. Three clusters of fractal dimension values corresponding to the main components of cerebellar tissue and average brightness values corresponding to them were determined: cerebellar white matter (70.684±0.473), granular layer of cortex (84.263±0.475), and molecular layer of cortex (96.263±0.449). The absence of certain clusters present in intact tissue and the presence of additional, pathological clusters may be criteria for diagnosing of the cerebellum using fractal analysis of magnetic resonance imaging of the brain