Radmila Gudović

Application of fractal analysis to neuronal dendritic arborisation patterns of the monkey dentate nucleus.

The deep nuclei of the cerebellar cortex have not yet received adequate exploratory attention. An exception is represented by the pioneering work of Chan-Palay, published in 1977, on the dentate nucleus morphology. She has classified each individual cell in the dentatus of the monkey into one of six types. Although fractal analysis is presently the most prominent quantitative method for morphometric neuronal studies, no article referring to applications of this method to the analysis of cell types of the dentate nucleus has so far been published. In the present study we apply fractal analysis to this unsolved problem and calculate the fractal dimension for each dendritic arbour of a neuron. We will hereby prove that by application of fractal analysis to the dendritic arbours of these cells whilst ignoring other neuronal attributes allows for clear discrimination of only three cell types.

FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.

Mathematical modelling of transformations of asymmetrically distributed biological data: An application to a quantitative classification of spiny neurons of the human putamen

Many measurements in biology follow distributions that can be approximated well by the normal distribution. The normal distribution plays an extremely important role in probability theory. However, some of the experimental data in biology are distributed asymmetrically. In order to transform such an asymmetrical distribution into a normal distribution, for which the standard statistical tables can be used for probability analysis of the available data, one must choose suitable transformation functions. We have met this problem when we qualitatively classified the spiny neurons in the adult human putamen. But, if one tries to test a qualitative classification of neurons quantitatively, a considerable class overlap between cells occurs as well as asymmetry often appears in the distributions of the data. We have already offered a method to overcome the overlapping problem when the data distributions are normal. In order to resolve the asymmetry problem in data distribution, we transformed our asymmetrically distributed data into an approximately normal distribution using a family of simple power functions and on a basis of appropriate probability analysis we propose a more acceptable classification scheme for the spiny neurons. The significance of our results in terms of current classifications of neurons in the adult human putamen is discussed.