Bratislav D. Stefanović

Morphology and classification of large neurons in the adult human dentate nucleus: A qualitative and quantitative analysis of 2D images

The dentate nucleus represents the most lateral of the four cerebellar nuclei that serve as major relay centres for fibres coming from the cerebellar cortex. Although many relevant findings regarding to the structure, neuronal morphology and cytoarchitectural development of the dentate nucleus have been presented so far, very little quantitative information has been collected on the types of large neurons in the human dentate nucleus. In the present study we qualitatively analyze our sample of large neurons according to their morphology and topology, and classify these cells into four types. Then, we quantify the morphology of such cell types taking into account seven morphometric parameters which describe the main properties of the cell soma, dendritic field and dendrite arborization. By performing appropriate statistics we prove out our classification of the large dentate neurons in the adult human. To the best of our knowledge, this study represents the first attempt of quantitative analysis of morphology and classification of the large neurons in the adult human dentate nucleus.

Fractal analysis of dendrite morphology using modified box-counting method

The box-counting dimension of a non-stellate neuron changes continuously with its rotation. During preprocessing for box-counting, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel. A non-stellate neuronal picture should have the smallest fractal dimension when the angle between the horizontal axis and its major diameter is about 45°. The box-counting method does not consider the position of a picture on the computer screen. Therefore a dispersion of the box dimension values of a neuronal sample is rather large and their mean value is with larger variance. Modified box-counting method partly diminishes these findings. To improve a dependence of neuronal rotation on the box-counting dimension of non-stellate neurons, prior to applying box-counting method, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel.

Mathematical modeling and computational analysis of neuronal cell images: Application to dendritic arborization of Golgi-impregnated neurons in dorsal horns of the rat spinal cord

Neurons of the rat spinal cord have been stained using the Golgi impregnation method. Successfully impregnated neurons from laminae I to VI were subjected to a computational analysis for complexity of dendritic tree structure. The analysis was performed using ruler-counting and circle-counting techniques. Our analysis aimed to support quantitatively the general concept of Rexeds laminar scheme of the dorsal horn of mammals. For that purpose, we have developed two mathematical models of neuronal arborization patterns, whose solutions yielded the inverse power-law and generalized power-law scaling. The latter comprises two main parameters: (i) the anfractuosity, characterizing the degree of dendritic complexity and (ii) an estimate of the total length of arbor dendrites. The anfractuosity can distinguish among the sets of drawings over all six laminae.

Fractal dimension of apical dendritic arborization differs in the superficial and the deep pyramidal neurons of the rat cerebral neocortex

Pyramidal neurons of the mammalian cerebral cortex have specific structure and pattern of organization that involves the presence of apical dendrite. Morphology of the apical dendrite is well-known, but quantification of its complexity still remains open. Fractal analysis has proved to be a valuable method for analyzing the complexity of dendrite morphology. The aim of this study was to establish the fractal dimension of apical dendrite arborization of pyramidal neurons in distinct neocortical laminae by using the modified box-counting method. A total of thirty, Golgi impregnated neurons from the rat brain were analyzed: 15 superficial (cell bodies located within lamina II-III), and 15 deep pyramidal neurons (cell bodies situated within lamina V-VI). Analysis of topological parameters of apical dendrite arborization showed no statistical differences except in total dendritic length (p=0.02), indicating considerable homogeneity between the two groups of neurons. On the other hand, average fractal dimension of apical dendrite was 1.33±0.06 for the superficial and 1.24±0.04 for the deep cortical neurons, showing statistically significant difference between these two groups (p<0.001). In conclusion, according to the fractal dimension values, apical dendrites of the superficial pyramidal neurons tend to show higher structural complexity compared to the deep ones.

The acidophilic nature of neuronal Golgi impregnation.

The mechanisms of Golgi impregnation of neurons has remained enigmatic for decades. Recently, it was suggested that divalent (di)chromate anions play a role in the Golgi impregnation process. Therefore, we incubated slices of (para)formaldehyde-fixed rat brain tissue in solutions of potassium (di)chromate, phosphate, chloride or nitrate at pH 6 or 7. Slices were then immersed in solutions of silver nitrate and processed for light microscopical analysis. At pH 6, dichromate probes resulted in dense and homogeneous impregnation of neuronal cytoplasm (typical impregnation). At pH 7, chromate probes showed solely partial cytoplasmic and heavy nuclear-region neuron impregnation (atypical impregnation). Phosphate probes at pH 6 resulted in typical impregnation, whereas at pH 7 phosphate probes gave atypical impregnation. Both at pH 6 and 7, chloride and nitrate probes did not yield any Golgi impregnation. These findings confirmed the pH-dependence of silver-chromate Golgi impregnation as well as the correctness of corresponding acidic silver-phosphate impregnation. Our study revealed a previously unknown, strong anion-dependence of Golgi impregnation, suggesting that hydrogenated monovalent anions are carriers of the neuron impregnation.

Modified Richardson's method versus the box-counting method in neuroscience

BACKGROUND The morphology of dendrites, including apical dendrites of pyramidal neurons, is already well-known. However, the quantification of their complexity still remains open. Fractal analysis has proven to be a valuable method of analyzing the degree of complexity of dendrite morphology. NEW METHOD Richardsons method is a technique of measuring the fractal dimension of open and closed lines of objects. This method was modified in order to measure the fractal dimension of neuronal arborization. The focus of this experiment was on the apical dendrites of superficial and deep pyramidal neurons in the rat cerebral cortex. RESULTS Apical dendrites of superficial cortical pyramidal neurons have a higher mean value of the fractal dimension as compared to deep pyramidal neurons. COMPARISON WITH EXISTING METHOD Using the modified Richardsons method we showed that the mean value of the fractal dimension of apical dendrites in superficial pyramidal neurons is highly statistically significant as compared to the value of the fractal dimension in deep pyramidal neurons. On the other hand, the mean values of the fractal dimension between the same groups of apical dendrites measured by the most popular box-counting method showed merely a statistically significant difference. CONCLUSION The modified Richardsons method of fractal analysis is an efficient mathematical method for calculating the fractal dimension of dendrites and could be used in order to calculate the complexity of dendrite arborization.

Fractal analysis of dendrites morphology using modified Richardson's and box counting method.

Fractal analysis has proven to be a useful tool in analysis of various phenomena in numerous naturel sciences including biology and medicine. It has been widely used in quantitative morphologic studies mainly in calculating the fractal dimension of objects. The fractal dimension describes an objects complexity: it is higher if the object is more complex, that is, its border more rugged, its linear structure more winding, or its space more filled. We use a manual version of Richardsons (ruler-based) method and a most popular computer-based box-counting method applying to the problem of measuring the fractal dimension of dendritic arborization in neurons. We also compare how these methods work with skeletonized vs. unskeletonized binary images. We show that for dendrite arborization, the mean box dimension of unskeletonized images is significantly larger than that of skeletonized images. We also show that the box-counting method is sensitive to an objects orientation, whereas the ruler-based dimension is unaffected by skeletonizing and orientation. We show that the mean fractal dimension measured using the ruler-based method is significantly smaller than that measured using the box-counting method. Whereas the box-counting method requires defined usage that limits its utility for analyzing dendritic arborization, the ruler-based method based on Richardsons model presented here can be used more liberally. Although this method is rather tedious to use manually, an accessible computer-based implementation for the neuroscientist has not yet been made available.