Nemanja Rajkovic

Mathematical modeling of the neuron morphology using two dimensional images.

In this study mathematical analyses such as the analysis of area and length, fractal analysis and modified Sholl analysis were applied on two dimensional (2D) images of neurons from adult human dentate nucleus (DN). Using mathematical analyses main morphological properties were obtained including the size of neuron and soma, the length of all dendrites, the density of dendritic arborization, the position of the maximum density and the irregularity of dendrites. Response surface methodology (RSM) was used for modeling the size of neurons and the length of all dendrites. However, the RSM model based on the second-order polynomial equation was only possible to apply to correlate changes in the size of the neuron with other properties of its morphology. Modeling data provided evidence that the size of DN neurons statistically depended on the size of the soma, the density of dendritic arborization and the irregularity of dendrites. The low value of mean relative percent deviation (MRPD) between the experimental data and the predicted neuron size obtained by RSM model showed that model was suitable for modeling the size of DN neurons. Therefore, RSM can be generally used for modeling neuron size from 2D images.

Effect of viscosity on the wave propagation: Experimental determination of compression and expansion pulse wave velocity in fluid-fill elastic tube

The velocity by which the disturbance travels through the medium is the wave velocity. Pulse wave velocity is one of the main parameters in hemodynamics. The study of wave propagation through the fluid-fill elastic tube is of great importance for the proper biophysical understanding of the nature of blood flow through of cardiovascular system. The effect of viscosity on the pulse wave velocity is generally ignored. In this paper we present the results of experimental measurements of pulse wave velocity (PWV) of compression and expansion waves in elastic tube. The solutions with different density and viscosity were used in the experiment. Biophysical model of the circulatory flow is designed to perform measurements. Experimental results show that the PWV of the expansion waves is higher than the compression waves during the same experimental conditions. It was found that the change in viscosity causes a change of PWV for both waves. We found a relationship between PWV, fluid density and viscosity.

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.

Richardson's Method of Segment Counting versus Box-Counting

Fractal analysis has become a popular method in all branches of scientific investigation including biology and medicine. This paper presents solution for many unresolved questions about the methodology of fractal theory, precisely in connection between fractal geometry and fractal analysis. While some concepts in fractal theory are determined descriptively and/or qualitatively, this paper provides their exact mathematical definition or explanation. Also, we present results in applying two basic length-related methods on two dimensional neuronal images and discuss their applicability.

Histological Images of Malignant Breast Tumor: Mono and Multifractal Analysis

Current breast cancer risk prognosis methods have high prognostic variability which affects the chemotherapy decisions. Image analysis is a structure analysis tool that aids existing risk prognosis methods in order to improve quality of the prognosis. Fractal image analysis has been rarely used on breast tumor histology images for prognostic purposes and this paper deals with one such study using monofractal and multifractal analysis. Invasive breast tumor histology samples were used based on the absence of any systemic treatment. Obtained images were divided into two groups, named high and low risk, based on the risk prognosis for survival. Images were further subjected to computational analysis using binary and outline fractal dimensions, lacunarity for monofratal analysis and generalized dimension for multifractal analysis. Binary and outline fractal dimensions, as well as generalized dimension yielded statistically significant distinction between high risk and low risk groups. Lacunarity was also different but not statistically significant.

The Pan-Cytokeratin Staining Intensity and Fractal Computational Analysis of Breast Tumor Malignant Growth Patterns Prognosticate the Occurrence of Distant Metastasis

Improved prognosis of breast cancer outcome could prolong patient survival by reliable identification of patients at high risk of metastasis occurrence which could benefit from more aggressive treatments. Based on such clinical need, we prognostically evaluated the malignant cells in breast tumors, as the obvious potential source of unexploited prognostic information. The patient group was homogeneous, without any systemic treatments or lymph node spread, with smaller tumor size (pT1/2) and a long follow-up. Epithelial cells were labeled with AE1/AE3 pan-cytokeratin antibody cocktail and comprehensively analyzed. Monofractal and multifractal analyses were applied for quantification of distribution, shape, complexity and texture of malignant cell clusters, while mean pixel intensity and total area were measures of the pan-cytokeratin immunostaining intensity. The results surprisingly indicate that simple binary images and monofractal analysis provided better prognostic information then grayscale images and multifractal analysis. The key findings were that shapes and distribution of malignant cell clusters (by binary fractal dimension; AUC = 0.29), their contour shapes (by outline fractal dimension; AUC = 0.31) and intensity of the pan-cytokeratin immunostaining (by mean pixel intensity; AUC = 0.30) offered significant performance in metastasis risk prognostication. The results reveal an association between the lower pan-cytokeratin staining intensity and the high metastasis risk. Another interesting result was that multivariate analysis could confirm the prognostic independence only for fractal but not for immunostaining intensity features. The obtained results reveal several novel and unexpected findings highlighting the independent prognostic efficacy of malignant cell cluster distribution and contour shapes in breast tumors.

Computational RSM modelling of dentate nucleus neuron 2D image surface

Abstract Backgrounds: The aim of this study is to model 2D dentate nucleus neuron surface (2D DNNIS) using the RSM modelling method and show in general such a modelling approach. Additionally, an application is made to the neurons of dentate nucleus lamina, namely VLL and DML. Methods: response surface methodology (RSM). Results: Several modelling formula are obtained. Models are classified according to neuron samples on which are obtained and number of factors used. Thus, in general, constrained and non-constrained, VLL and DML models are analysed. Obtained non-constrained models are quadratic model with multifactor interaction for all samples (adjusted R2 0.96) and VLL sample (adjusted R2 0.98) and linear model with multifactor interaction for DML sample (adjusted R2 0.95). Constrained models are bifactor models, namely general one without factor interaction with adjusted R2 0.93; and for particular lamina, the models are accompanied with factor interaction (adjusted R2 0.95). Conclusion: Though it is of the smallest adjusted R2 (0.93), constrained general model is shown to be the most promising one for modelling 2D neuron surface for adult DNN.

Box-Counting Method in Quantitative Analysis of Images of the Brain

The introduction of fractal geometry in the neurosciences has been a major paradigm shift over the last decades as it has helped overcome approximations and limitations that occur when reductionist approaches are used to analyze neurons or the entire brain. Fractal geometry allows for quantitative analysis and description of the geometric complexity of the brain, particularly fractal analysis provides a quantitative tool for the study of morphology of brain cells and the brain structure itself. The box-counting method of fractal analysis, its modification are presented on 2D image of neurons from the monkey brain. The use of MATLAB software, particularly when the 2D or 3D image of the brain have to be quantified with box-counting procedure is also presented. This paper offers a link between the applications of fractal analysis to the neuroanatomy and basic neurosciences with the clinical applications.

Analysis of Histopathology Images by the Use of Monofractal and Multifractal Algorithms

The complexity of breast cancer histological images carries the information that could be useful in prognosis of metastatic occurrences. Computational tumour histomorphology analysis is a novel tool that aims to complement current prognostic approaches. This paper deals with the direct comparison of the prognostic value of different image formats and different image analysis algorithms. Generalizability of the methodology is investigated by the use of the two groups of patients. Binary and grayscale images of tumour histology samples from both patient groups were subjected to mono and multifractal analysis. On the basis of the obtained area under the curve values as a measure of features association with a disease outcome, it can be concluded that analysis of greyscale images delivered a far better performance in comparison to the analysis of binary images. Also, it should be noted that for different patient groups, algorithms were not equally successful which calls for further investigation.