Characterization of white matter branching in human cerebella: quantitative morphological assessment and fractal analysis of skeletonized MR images

Abstract

Introduction: The aim of the present study was to investigate branching characteristics of the human cerebellar white matter by the means of findings obtained from the quantitative morphological assessment and fractal analysis of the skeletonized MR images of the human cerebellum.
 Methods: Thirty individuals with no apparent brain pathology (15 males and 15 females, ranging from 18 - 30 years of age) participated in this study. Their normal T2-weighted MR images of the cerebellar vermis (midsagittal plane) were examined. The skeletonizing procedure and subsequent quantitative morphological assessment of the acquired skeletonized MR images were performed. The following parameters were determined: the number of branches, the number of junctions, the amount of end-point voxels, junction voxels and slab voxels, the average and maximum branch lengths, the longest-shortest patch length, and the number of triple and quadruple points. Additionally, the individual branches of the obtained digital skeletons of the cerebellar white matter were examined and the following parameters were assessed: branch length variability, Euclidean distance, and branch length/Euclidean distance ratio. A fractal analysis was performed using the box counting method prior to and after the MR image skeletonizing procedure. The values of the fractal dimensions (FD) of both skeletonized and non-skeletonized MR images were calculated.
 Results: It was established that the cerebella, which had the maximum values of the FD, possessed a large number of small branches approximately equal in length and which were connected by numerous junctions, forming numerous endpoints. Those cerebella, which had higher values of the average branch length and greater branch length variability, showed lower values of the FD. The key characteristics of the digital skeleton that determined the values of the FD of the cerebellum and its skeletonized MR images were the number of branches and the number of junctions that had the strongest correlational relationships with the FD of the skeletonized MR images. We submitted a proposition to consider the number of branches and amount of junctions as a diagnostic criterion in the determination of normal values of the FD.
 Conclusions: The obtained data can be used as diagnostic criteria in assessment of the morphofunctional state of the cerebellum using magnetic resonance imaging (MRI) technique.

Shape of cerebral hemispheres: structural and spatial complexity. Quantitative analysis of skeletonized MR images

“…Conversely, the digital skeletons of the hemispheres, which have a less complex configuration, have smaller values of fractal dimension and consist of a small number of relatively long branches. Similar regularities were also revealed as a result of quantitative analysis of skeletonized images of cerebellar white matter [15].…”

“…For the quantitative characterization of spatial and structural complexity, such a quantity as the fractal dimension is used, which is determined by means of fractal analysis [14]. Using this method, research was carried out on the cortex of the cerebral hemispheres [4,10,24] and its outer surface [8,11], as well as the white matter of the cerebral hemispheres [3,5,19,21,22,[26][27][28] and cerebellar white matter [13,15].…”

“…Quantitative analysis of skeletonized images was used in the study of tree-like structures (most often -the dendritic tree of neurons) [7,17,18]. Previously, we performed a quantitative analysis of skeletonized images of human cerebellar white matter [15]. However, according to the scientific literature available to us, quantitative analysis of skeletonized images of the cerebral hemispheres has not been performed before.…”

A novel women's ovulation prediction through salivary ferning using the box counting and deep learning

“…Fractal analysis is a mathematically independent and experimental method based on the mandelbrot fractal geometry, traditional euclidean experimental geometry, and the richardson coastline method. Morphometrics is an integral part of most modern morphological studies, which are widely used in research in the field of medicine [9]. In the last decade, the principles, parameters, and methods of fractal geometry have been increasingly used in morphological studies rather than euclidean geometry.…”

Cytoarchitecture of Cerebellar Cortex: Fractal Analysis as a Method for Quantitative Studies

“…This method is used for studies of cerebral [13,15,16] and cerebellar [17][18][19] structures (white matter and cortex) and as an additional morphometric method in neuroimaging. In our previous studies we determined fractal dimension values of skeletonized images of cerebral hemispheres [20,21] and cerebellar white matter [22]. Fractal analysis also is used on microscopic level of brain organization: it was used for the quantitative studies of neuronal dendritic arborizations [22][23][24][25][26], astrocytes [27,28] and microglial cells [29].…”