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.

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.

Mathematical model of neuronal morphology: prenatal development of the human dentate nucleus.

The aim of the study was to quantify the morphological changes of the human dentate nucleus during prenatal development using mathematical models that take into account main morphometric parameters. The camera lucida drawings of Golgi impregnated neurons taken from human fetuses of gestational ages ranging from 14 to 41 weeks were analyzed. Four morphometric parameters, the size of the neuron, the dendritic complexity, maximum dendritic density, and the position of maximum density, were obtained using the modified Scholl method and fractal analysis.

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°.

Fractal analysis of dendrite morphology of rotated neuronal pictures: the modified box counting method.

The fractal dimension of a non-stellate neuron changes continuously with rotation of the neuronal picture. For a stellate neuron such changes cannot be noticed. During preprocessing for the box counting, non-stellate neurons should be arranged so that the major diameters of their dendrite fields are parallel.

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 object's 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.

Neuronal images of the putamen in the adult human neostriatum: a revised classification supported by a qualitative and quantitative analysis.

A qualitative analysis of the morphology of human putamen nerve cells involves a detailed description of the structure and features of neurons and, accordingly, their classification into already defined classes and types. In our sample of 301 neurons, 64.78 % (195) were spiny and 35.

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.

Fractal analysis: methodologies for biomedical researchers.

Fractal analysis has become a popular method in all branches of scientific investigations including biology and medicine. Although there is a growing interest in the application of fractal analysis in biological sciences, questions about the methodology of fractal analysis have partly restricted its wider and comprehensible application. It is a notable fact that fractal analysis is derived from fractal geometry, but there are some unresolved issues that need to be addressed.

The morphology and classification of α ganglion cells in the rat retinae: a fractal analysis study.

Rat retinal ganglion cells have been proposed to consist of a varying number of subtypes. Dendritic morphology is an essential aspect of classification and a necessary step toward understanding structure-function relationships of retinal ganglion cells. This study aimed at using a heuristic classification procedure in combination with the box-counting analysis to classify the alpha ganglion cells in the rat retinae based on the dendritic branching pattern and to investigate morphological changes with retinal eccentricity.

On the classification of normally distributed neurons: an application to human dentate nucleus.

One of the major goals in cellular neurobiology is the meaningful cell classification. However, in cell classification there are many unresolved issues that need to be addressed. Neuronal classification usually starts with grouping cells into classes according to their main morphological features.

[Quantitative analysis of dendritic branching pattern of large neurons in human cerebellum].

Background/aim: Dentate nucleus (nucleus dentatus) is the most distant of the cerebellar nuclei and the major system for information transfer in the cerebellum. So far, dendritic branches of four different kinds of large neurons of dentate nucleus, have been considered mainly qualitatively with no quantification of their morphological features. The aim of the study was to test the qualitative hypothesis that the human dentate nucleus is composed of various types of the large neurons by quantitative analysis of their dendritic branching patterns.

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.

Morphology and cell classification of large neurons in the adult human dentate nucleus: a quantitative study.

The dentate nucleus represents the most lateral of the four cerebellar nuclei that serve as a major relay centres for fibres coming from the cerebellar cortex. Although many relevant findings regarding to the three-dimensional structure, the neuronal morphology and the cytoarchitectural development of the dentate nucleus have been presented so far, very little quantitative information has been collected to further explain several types of large neurons in the dentate nucleus. In this study we quantified the morphology of the large dentate neurons in the adult human taking, into account seven morphometric parameters that describe the main properties of the cell soma, the dendritic field and the dendritic branching pattern.

Cell image area as a tool for neuronal classification.

The measurement of the area of a shapeless plane region is one of the basic problems in traditional calculus. In order to calculate the 'true' area of such a region, we have superimposed a net of identical squares on this region, counted the squares containing at least one point of the region, and calculated the sum of the areas of said squares. This sum represents an approximation of the region's area.

Quantitative analysis of dendritic morphology of the α and δ retinal ganglion cells in the rat: a cell classification study.

Type I retinal ganglion cells in the rat have been classified into several groups based on the cell body size and dendritic morphology. Considerable overlap and heterogeneity within groups have been reported, which is especially obvious for the morphology of the dendritic tree. For that purpose, we analysed quantitatively the dendritic morphology of the alpha and delta rat retinal ganglion cells, using parameters which provide information on the dendritic field size, shape of the dendritic tree and dendritic branching complexity.

Mathematical modelling of neuronal dendritic branching patterns in two dimensions: application to retinal ganglion cells in the cat and rat.

Sholl's analysis has been used for about 50 years to study neuron branching characteristics based on a linear, semi-log or log-log method. Using the linear two- dimensional Sholl's method, we call attention to a relationship between the number of intersections of neuronal dendrites with a circle and the numbers of branching points and terminal tips encompassed by the circle, with respect to the circle radius. For that purpose, we present a mathematical model, which incorporates a supposition that the number of dendritic intersections with a circle can be resolved into two components: the number of branching points and the number of terminal tips within the annulus of two adjoining circles.

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.

A confirmation of Rexed's laminar hypothesis using the Sholl linear method complemented by nonparametric statistics.

Images of Golgi-impregnated neurons from laminae I to VI in the dorsal horn of the cat spinal cord were subjected to the linear Sholl analysis of concentric circles to support Rexed's hypothesis on the laminar organization of spinal gray matter in mammals. Since Rexed's determination of the laminae is based upon size, location, and grouping of cell bodies, neglecting one of the principal morphologic attributes of the neuron-the dendritic tree, the purpose of the present study was to evaluate Rexed's hypothesis testing the structure of dendritic arborization patterns of neurons. The differences in the complexity of dendritic trees between the groups of neurons from different laminae were evaluated by nonparametric statistics.

The Sholl analysis of neuronal cell images: semi-log or log-log method?

Although the Sholl analysis is a quantitative method for morphometric neuronal studies and its application provides many benefits to neurobiology since it is obvious, common and meaningful, there are many unresolved theoretical issues that need to be addressed. Nevertheless, it can be practiced without much background or sophistication. The two different methods of the Sholl analysis--log-log and semi-log--have been applied previously without a clear basis as to what to use.

Application of modified Sholl analysis to neuronal dendritic arborization of the cat spinal cord.

The drawings of Golgi-impregnated neurons from laminae I to VI in dorsal horn of the cat spinal cord were analysed morphometrically with a modified Sholl method of concentric circles. In order to advance the Sholl analysis of neuronal dendritic arborization patterns, we developed a new method of data presentation using polynomial regression and defining three parameters: the critical value of the circle radius (which defines the place of a possible circle intersecting maximum number of dendrites), the maximum number of dendritic intersections with the circles (counted for consecutive circles placed starting at the cell body to the border of the dendritic tree), and the mean value of the fitted polynomial function (which describes an average property concerning numbers of branches of dendritic tree over the whole region occupied by the dendritic arbor). For that purpose we also used the Sholl regression coefficient as well as the Schoenen ramification index.

Fractality of dendritic arborization of spinal cord neurons.

Skeletonized images of Golgi impregnated neurons from the human, monkey, cat and rat dorsal horns were subjected to fractal analysis. These neurons have sparse branching of dendrite arbors. It is noticed that, in certain neuronal samples, some authors report that scaling range of experimentally declared fractals is extremely limited and spanned approximately between 0.

[Morphometric analysis of neurons from the marginal and substantia gelatinosa layers of human spinal cord: classification according to laminar organization].

The main goal of morphometric analysis of neuronal images, except for getting information about their geometry and dendritic branching patterns, is their classification based on laminar organization. The majority of contemporary techniques for image analysis are based on the application of fractal theory, which has some limitations on results analysis. For that reasons, the new, mostly nonfractal techniques for image analysis had been designed in the past few years.

[Topography and asymmetry of the visual response in electroencephalographic power spectra in healthy children].

In order to quantify the visual reactivity of EEG to opening the eyes, the topography of EEG power spectra in a sample of 72 healthy subjects aged from 7-15 years, was studied. The EEGs were recorder at 14 scalp sites under eyes closed (ECL) and eyes open (EOP). It has been established that the absolute powers in total and in alpha band were significantly higher in all derivations under ECL as compared with EOP condition.