Bojana Krstonošić

Box-Counting and Multifractal Analysis in Neuronal and Glial Classification

Fractal analysis in the neurosciences has advanced over the past twenty years. The fractal dimension, besides its ability to discriminate among different cell types, can work as a reliable parameter in cell classification. A qualitative analysis of the morphology of neurons and glia cell types involves a detailed description of the structure and features of cells, and accordingly, their classification into defined classes and types. This paper outlines how fractal analysis can be used for further quantitative classification of these cell types using box-counting and multifractal analysis.

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.

Box-Counting Method of 2D Neuronal Image: Method Modification and Quantitative Analysis Demonstrated on Images from the Monkey and Human Brain

This study calls attention to the difference between traditional box-counting method and its modification. The appropriate scaling factor, influence on image size and resolution, and image rotation, as well as different image presentation, are showed on the sample of asymmetrical neurons from the monkey dentate nucleus. The standard BC method and its modification were evaluated on the sample of 2D neuronal images from the human neostriatum. In addition, three box dimensions (which estimate the space-filling property, the shape, complexity, and the irregularity of dendritic tree) were used to evaluate differences in the morphology of type III aspiny neurons between two parts of the neostriatum.

Box-Count Analysis of Two Dimensional Images: Methodology, Analysis and Classification

This paper calls attention to the methodology issues of the box-counting method, precisely, to the scaling procedure and significance of the parameter calculated for different presentation of the same image. By using basic terms of fractal analysis and statistical assessment of correlation coefficients of a straight line fit, we showed correct choice for the size of boxes. Moreover, we showed correct box-count dimension in case of neurons with sparse or thick dendrites and small or large cell bodies. In addition, this paper presents our main results relating to the quantitative study and classification of 2D images from the monkey cerebral cortex and the human caudate nucleus.

The neuromorphological caudate–putaminal clustering of neostriate interneurons: Kohonen self–organizing maps and supervised artificial neural networks with multivariate analysis

AIMS The objective of this study is to investigate the possibility of the neuromorphotopological clustering of neostriate interneurons (NSIN) and their consequent classification into caudate (CIN) and putaminal neuron type (PIN), according to the nuclear localization of the neurons. It tends to discover whether these two topological neuron types are morphologically different. MATERIAL AND METHODS The binary images of adult human NSIN are used for the purposes of the analysis. The total of the 46 neuromorphological parameters is used. They can be divided into the following classes: neuron surface/size, shape, compartmental length, dendritic branching, neuromorphological organization and complexity. The clustering is performed by an algorithm which consists of the steps of predictor extraction, multivariate cluster analysis set and cluster identification. RESULTS Unifactor analysis extracted as significant the following parameters: neurosoma/perikaryon size (AS), the size of a dendritic tree (ADT), the size of a dendritic field area (ADF), the size of an entire neuron field area (ANF), the size of a perineuronal space (APNS), the fractal dimension of a neuron (DN), the index of perikaryon asymmetry (MS), total dendritic length (L), standardized total dendritic length (Lst), standardized dendritic width (DWDTHst), dendritic centrifugal branching order (DCBO), branching polarization index (MDCBO), dendritic partial surface (DSP), the fractal dimension of a skeletonized neuron image (DS), the index of maximal complex density of a dendritic tree (NMAX) and standardized dendritic branching pattern complexity (CDF/ADFst). The cluster analysis set together with Kohonen self-organizing maps and backpropagation feed-forward artificial neural networks confirmed the classification on both unsupervised and supervised manner, respectively. As a final step, the cluster identification is performed by an assignment of each neuron to a particular cluster. CONCLUSION NSIN can be classified neuromorphologically into CIN and PIN type. Differences are expected since the two nuclei have different functional roles in processing the information involved in volitional movement control.

The translaminar neuromorphotopological clustering and classification of the dentate nucleus neurons

Thisstudy aims to determine whether dentate neurons can be translaminarlyneuromorphotopologically classified as ventrolateral or dorsomedial type. Adulthuman dentate interneuron 2D binary images are analyzed. The analysis isperformed on both real and virtual neuron samples and 29 parameters are used.They are divided into the classes: neuron surface, shape, length, branching andcomplexity. Clustering is performed by an algorithm that employs predictor extraction (matrix attractor analysis/non-negative matrix factorization and cluster analysis of predictor factors - separate unifactor analysis/Student’s t-test and MANOVA) and multivariate cluster analysis (cluster analysis, principal component analysis, factor analysis with pro/varimax rotation, Fisher’s linear discriminant analysis and feed-forward backpropagation artificial neural networks). The separate unifactor analysis extracted as significant the following predictors from the natural cell sample: the Npd (p< 0:05), and from the virtual cell sample: the Adt (p< 0.05),Do (p< 0.001), Ms (p< 0.01), Dwdth (p< 0:001), Npd (p< 0:05), Nsd (p< 0.001), Nt/hod (p< 0.001), Nmax (p< 0.01), Ds (p< 0.001), Cdf (Nt/hod)st (p< 0.05). For the multidimensional analysis, with the exception of the Fisher’s linear discriminant analysis which gave a false positive result, all other analyses rejected the translaminar dentate neuron classification. Thus, dentate neurons cannot be classified into ventrolateral/dorsomedial neuromorphotopological subtypes. Although some differences were found to exist, they are not sufficient to carry this classification. The methods of multidimensional statistical analysis are again shown to be the best for such kinds of analysis.

Anatomical variations of the human occipital condyles

Occipital condyles, located at the inferior sides of lateral parts of occipital bone, are important structures that connect the cranium and the vertebral column. Their size, shape, location and, also, their congruence with superior articular facets of the atlas vertebra are of great importance for the stability of craniovertebral junctions. The progress in medical diagnostic and surgical techniques in the area of foramen magnum, requires the knowledge regarding anatomical aspects of this region. The purpose of this study was to evaluate the measurements of the occipital condyles, as well as to analyse the variations in the shape of the condyles and their position in relation to the foramen magnum. This study included 25 adult human skulls (11 male and 14 female) from the Osteological collection of the Department of Anatomy at Medical Faculty in Novi Sad. Nine parameters, which define morfological properties of the occipital condyles, were measured using Vernier caliper. Also, the shape and location of the condyles, as well as the narrowness of the foramen magnum were described. Our findings show that length of the left occipital condyle, as well as distance between the posterior top of the left occipital condyle and basion are statistically greater in male crania, comparing to female crania. According to the shape of the occipital condyles, we classified them in seven groups. Predominant type is oval shaped. The condylar foramen is bilaterally present in 36 % and the occipital condyles bilaterally protrude the foramen magnum in 40 % of analyzed crania. Morphometric analysis of the occipital condyles showed variations in their size, shape, presence of condylar canal and relation to the foramen magnum.