Analysis of Spatial Distribution and Prognostic Value of Different Pan Cytokeratin Immunostaining Intensities in Breast Tumor Tissue Sections.

Cancer risk prognosis could improve patient survival through early personalized treatment decisions. This is the first systematic analysis of the spatial and prognostic distribution of different pan cytokeratin immunostaining intensities in breast tumors. The prognostic model included 102 breast carcinoma patients, with distant metastasis occurrence as the endpoint. We segmented the full intensity range (0-255) of pan cytokeratin digitized immunostaining into seven discrete narrow grey level ranges: 0-130, 130-160, 160-180, 180-200, 200-220, 220-240, and 240-255. These images were subsequently examined by 33 major (GLCM), fractal and first-order statistics computational analysis features. Interestingly, while moderate intensities were strongly associated with metastasis outcome, high intensities of pan cytokeratin immunostaining provided no prognostic value even after an exhaustive computational analysis. The intense pan cytokeratin immunostaining was also relatively rare, suggesting the low differentiation state of epithelial cells. The observed variability in immunostaining intensities highlighted the intratumoral heterogeneity of the malignant cells and its association with a poor disease outcome. The prognostic importance of the moderate intensity range established by complex computational morphology analyses was supported by simple measurements of its immunostaining area which was associated with favorable disease outcome. This study reveals intratumoral heterogeneity of the pan cytokeratin immunostaining together with the prognostic evaluation and spatial distribution of its discrete intensities.

Comparison of Monofractal, Multifractal and gray level Co-occurrence matrix algorithms in analysis of Breast tumor microscopic images for prognosis of distant metastasis risk.

Breast cancer prognosis is a subject undergoing intense study due to its high clinical relevance for effective therapeutic management and a great patient interest in disease progression. Prognostic value of fractal and gray level co-occurrence matrix texture analysis algorithms has been previously established on tumour histology images, but without any direct performance comparison. Therefore, this study was designed to compare the prognostic power of the monofractal, multifractal and co-occurrence algorithms on the same set of images. The investigation was retrospective, with 51 patients selected on account of non-metastatic IBC diagnosis, stage IIIB. Image analysis was performed on digital images of primary tumour tissue sections stained with haematoxylin/eosin. Bootstrap-corrected Cox proportional hazards regression P-values indicated a significant association with metastasis outcome of at least one of the features within each group. AUC values were far better for co-occurrence (0.66-0.77) then for fractal features (0.60-0.64). Correction by the split-sample cross-validation likewise indicated the generalizability only for the co-occurrence features, with their classification accuracies ranging between 67 and 72 %, while accuracies of monofractal and multifractal features were reduced to nearly random 52-55 %. These findings indicate for the first time that the prognostic value of texture analysis of tumour histology is less dependent on the morphological complexity of the image as measured by fractal analysis, but predominantly on the spatial distribution of the gray pixel intensities as calculated by the co-occurrence features.

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.

Incipient UV-Induced Structural Changes in Neutrophil Granulocytes: Morphometric and Texture Analysis of Two-Dimensional Digital Images.

The aim of this study is to determine the ability and consequent significance of fractal and lacunarity analysis together with computational morphometric and gray-level co-occurrence matrix (GLCM) analysis in detecting subtle initial UVB-induced chromatin and cytosolic changes in neutrophil granulocytes. In addition, the direction and potential significance of the observed changes is speculated. Feulgen-stained neutrophils are pictured and their digitalized images are analyzed in specialized software for digital image processing and ImageJ analysis. Significant statistical difference is observed (p0.05). For other parameters there was mostly high statistical significance (p>0.05). Significant unmatched correlations were found as sensitive markers of early morphological changes in cells exposed to UV light. In addition, the correlation between nuclear area and entropy was determined and was highly significant (p<0.001). UVB light, due to its high absorbance by DNA molecules, leads to double behavior of the cells. On one hand, cells start to rearrange but on the other UV light starts very early to immediately damage the cell. All these processes are very subtle in their intensity and GLCM analysis and computational imaging methods based on fractal geometry, i.e. fractal and morphometric analysis, in particular their combination, are very sensitive for detecting and describing these early chromatin changes.

Neurons from the adult human dentate nucleus: neural networks in the neuron classification.

OBJECTIVES: Topological (central vs. border neuron type) and morphological classification of adult human dentate nucleus neurons according to their quantified histomorphological properties using neural networks on real and virtual neuron samples. RESULTS: In the real sample 53.1% and 14.1% of central and border neurons, respectively, are classified correctly with total of 32.8% of misclassified neurons. The most important result present 62.2% of misclassified neurons in border neurons group which is even greater than number of correctly classified neurons (37.8%) in that group, showing obvious failure of network to classify neurons correctly based on computational parameters used in our study. On the virtual sample 97.3% of misclassified neurons in border neurons group which is much greater than number of correctly classified neurons (2.7%) in that group, again confirms obvious failure of network to classify neurons correctly. Statistical analysis shows that there is no statistically significant difference in between central and border neurons for each measured parameter (p>0.05). Total of 96.74% neurons are morphologically classified correctly by neural networks and each one belongs to one of the four histomorphological types: (a) neurons with small soma and short dendrites, (b) neurons with small soma and long dendrites, (c) neuron with large soma and short dendrites, (d) neurons with large soma and long dendrites. Statistical analysis supports these results (p<0.05). CONCLUSION: Human dentate nucleus neurons can be classified in four neuron types according to their quantitative histomorphological properties. These neuron types consist of two neuron sets, small and large ones with respect to their perykarions with subtypes differing in dendrite length i.e. neurons with short vs. long dendrites. Besides confirmation of neuron classification on small and large ones, already shown in literature, we found two new subtypes i.e. neurons with small soma and long dendrites and with large soma and short dendrites. These neurons are most probably equally distributed throughout the dentate nucleus as no significant difference in their topological distribution is observed.

Gray-Level Co-Occurrence Matrix Texture Analysis of Breast Tumor Images in Prognosis of Distant Metastasis Risk.

Owing to exceptional heterogeneity in the outcome of invasive breast cancer it is essential to develop highly accurate prognostic tools for effective therapeutic management. Based on this pressing need, we aimed to improve breast cancer prognosis by exploring the prognostic value of tumor histology image analysis. Patient group (n=78) selection was based on invasive breast cancer diagnosis without systemic treatment with a median follow-up of 147 months. Gray-level co-occurrence matrix texture analysis was performed retrospectively on primary tumor tissue section digital images stained either nonspecifically with hematoxylin and eosin or specifically with a pan-cytokeratin antibody cocktail for epithelial malignant cells. Univariate analysis revealed stronger association with metastasis risk by texture analysis when compared with clinicopathological parameters. The combination of individual clinicopathological and texture variables into composite scores resulted in further powerful enhancement of prognostic performance, with an accuracy of up to 90%, discrimination efficiency by the area under the curve [95% confidence interval (CI)] of 0.94 (0.87-0.99) and hazard ratio (95% CI) of 20.1 (7.5-109.4). Internal validation was successfully performed by bootstrap and split-sample cross-validation, suggesting that the models are generalizable. Whereas further validation is needed on an external set of patients, this preliminary study indicates the potential use of primary breast tumor histology texture as a highly accurate, simple, and cost-effective prognostic indicator of distant metastasis risk.

An anatomical study of the lumbar external foraminal ligaments: appearance at MR imaging.

PURPOSE: The purpose of this study was to examine the MRI appearance of the ligaments within the external space of the lumbar intervertebral foramen by correlating MR images with the corresponding anatomic dissection of the cadaver lumbar spine. METHODS: This was a two part study. Part I of the anatomic study consisted of the dissection of lumbar specimens from one embalmed adult male cadaver. At each lumbar level the external ligamentous structures were identified and their origin, insertion and position were determined. Part II of the study consisted of the anatomical analysis of the external transforaminal ligaments in the 180 lumbar intervertebral foramina on the MR images (1.5 T) in the sagittal plane. The diagnostic procedure was performed on 18 individuals from 18 to 25 years of age. RESULTS: The external transforaminal ligaments were observed at all levels and from both sides in the lumbar intervertebral foramen. The presence of the superior corporotransverse ligament was found in 45.56% intervertebral foramina, while the inferior corporotransverse ligament was found in 61.67% intervertebral foramina in the MRI. CONCLUSION: Our results confirm that external transforaminal ligaments are common structures in the intervertebral foramen. The results of this study show that the external transforaminal ligaments can be clearly visualized in MR images. It is crucial to have previous knowledge of the cadaveric specimens to recognize the transforaminal ligaments in MR images. The presence of these ligaments is clinically important because the ligaments could be the cause of nerve root compression or the low back pain syndrome.

Quantitative analysis of the Golgi impregnated human (neo)striatal neurons: Observation of the morphological characteristics followed by an emphasis on the functional diversity of cells.

BACKGROUND: The (neo)striatum is the major input structure of the basal nuclei, which is involved in the execution of voluntary movements, but also in controlling the processes that lead to the movement, such as motivation and cognition. The striatum provides its function through an interaction between projection neurons and interneurons. The aim of this study was to quantify the morphological properties of neurons in the precommissural putamen and precommissural caudate nucleus head and to evaluate whether there is a difference in cell morphology between different cell groups within one part and between the same cell groups within different parts of the striatum. METHODS: A total of 652 neuronal images of human striatum were observed. The features of the neuronal morphology (soma size, dendritic field size, shape of neuronal image, dendritic curviness, dendritic branching complexity) were observed by determining appropriate parameters of digital images of neurons. RESULTS: According to the presence of spines on the soma and/or dendrites, neurons were qualitatively classified into 446 spiny and 206 aspiny cells. The analysis of the distribution of the dendritic field area shows that spiny and aspiny neurons from both parts of the neostriatum can be decomposed into two distributions, which means that they can be classified into subgroups. A quantitative analysis of the spiny/aspiny neurons in the human putamen or caudate nucleus head has shown that there is a statistically significant difference between them. By comparing the morphology of neurons of the same group between different parts of the human neostriatum (putamen and caudate nucleus), it was also determined that there is a statistically significant difference. CONCLUSION: Since the morphology and function of neurons are in close correlation, it can be assumed that different groups of neurons in the human striatum might support functional diversity of the studied area.

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.

Changes in fractal dimension and lacunarity as early markers of UV-induced apoptosis.

The aim of our study was to employ fractal analysis for evaluation of ultrastructural changes during early stages of apoptosis. Apoptosis was induced in U251 human glioma cell line by exposure to UVB light. The cells were visualized by optical phase-contrast microscopy and photographed before the UV treatment, immediately after the treatment, as well as at 30 min intervals during 5h observation period. For each of the 32 cells analyzed, cellular and nuclear fractal dimension, as well as nuclear lacunarity, were determined at each time point. Our data demonstrate that cellular ultrastructural complexity determined by fractal dimension and lacunarity significantly decreases after the UV irradiation, with the nuclear lacunarity being a particularly sensitive parameter in detecting early apoptosis. Importantly, fractal analysis was able to detect cellular apoptotic changes earlier than conventional flow cytometric analysis of phosphatidylserine exposure, DNA fragmentation and cell membrane permeabilization. These results indicate that fractal analysis might be a powerful and affordable method for non-invasive early identification of apoptosis in cell cultures.

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. If one tries to test quantitatively such a qualitative classification, a considerable overlap in cell types often appears. There is little published information on it. In order to remove the above-mentioned shortcoming, we undertook the present study with the aim to offer a novel method for solving the class overlapping problem. To illustrate our method, we analyzed a sample of 124 neurons from adult human dentate nucleus. Among them we qualitatively selected 55 neurons with small dendritic fields (the small neurons), and 69 asymmetrical neurons with large dendritic fields (the large neurons). We showed that these two samples are normally and independently distributed. By measuring the neuronal soma areas of both samples, we observed that the corresponding normal curves cut each other. We proved that the abscissa of the point of intersection of the curves could represent the boundary between the two adjacent overlapping neuronal classes, since the error done by such division is minimal. Statistical evaluation of the division was also performed.

Classification by morphology of multipolar neurons of the human principal olivary nucleus.

The principal olivary nucleus is the largest part of the inferior olivary complex and is involved in the spatial and temporal organization of movement and motor learning. Nearly all neurons in this nucleus is multipolar along with having a highly complex dendritic tree and significant asymmetry in shape. In this study, we updated the current classification scheme, examined morphological differences between the proposed groups, and investigated age-related morphological changes. Histological preparations were digitized by a light microscope and a sample of 259 images of neurons was analyzed by 17 computationally generated parameters of morphology. These were reduced to the four variables of principal component analysis and the sample was classified by k-means method of clustering into three clusters. The differences between clusters were documented and for medium-sized neurons the relationship between four morphological parameters and age were investigated. Finally, for two of the age groups the changes in the morphology were explored. This study includes a detailed and robust classification of the PON neurons and the findings improve upon past qualitative work.

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. We show that the alpha and delta cells have significantly different dendritic field sizes. Taking into account the level of stratification of the dendritic tree, we found a difference in the properties of the dendritic morphology between alpha inner and alpha outer cells, while the opposite result was obtained for the delta inner and delta outer delta cells. In this study we also call attention to the relationship between morphological parameters and retinal eccentricity. The significance of our quantitative results in terms of present alpha and delta rat retinal ganglion cell classification is discussed.

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. The numbers of intersections and last two sets of data are also presented as cumulative frequency plots and analysed using a logistic model (Boltzmann's function). Such approaches give rise to several new morphometric parameters, such as, the critical, maximal and mean values of the numbers of intersections, branching points and terminal tips, as well as the abscissas of the inflection points of the corresponding sigmoid plots, with respect to the radius. We discuss these parameters as an additional tool for further morphological classification schemes of vertebrate retinal ganglion cells. To test the models, we apply them first to three groups of morphologically different cat's retinal ganglion cells (the alpha, gamma and epsilon cells). After that, in order to quantitatively support the classification of the rat's alpha cells into the inner and outer cells, we apply our models to two subgroups of these cells grouped according to their stratification levels in the inner plexiform layer. We show that differences between most of our parameters calculated for these subgroups are statistically significant. We believe that these models have the potential to aid in the classification of biological images.

Strawberry (Fragaria X ananassa Duch.) yield as affected by the soil pH.

Two-year trials (20062007) suggested that the use of calcium oxide (CaO) on acid soils increased soil pH and yields in strawberry cultivars Marmolada, Selena and Senga Sengana, under the environmental conditions of Cacak (Western Serbia). The highest yield was obtained when CaO was applied at 750 kg ha-1 rate. Further increase in rate up to 1,500 kg ha-1 did not show corresponding increase in yield; the result was a slight yield drop compared to the peak yield shown at 750 kg ha(1) rate. Overall, yields at rates above 750 kg ha(1) were still higher than control and in the treatment employing lowest CaO application rate of 250 kg ha-1.

Aspergillus fumigatus branching complexity in vitro: 2D images and dynamic modeling.

BACKGROUND: Aspergillus fumigatus causes serious infections in humans, and its virulence correlates with hyphal growth, branching and formation of the filamentous mycelium. The filamentous mycelium is a complex structure inconvenient for quantity analysis. In this study, we monitored the branching of A. fumigatus filamentous mycelium in vitro at different points in time in order to assess the complexity degree and develop a dynamic model for the branching complexity. METHOD: We used fractal analysis of microscopic images (FAMI) to measure the fractal dimensions (D) of the branching complexity within 24 h of incubation. RESULTS: By photographing the filamentous mycelium dynamically and processing the images, the D variation curve of A. fumigatus complexity degree was obtained. We acquired the D variation curve which contained initial exponential period and stationary period of A. fumigatus branching. Further, the obtained data of D was modeled via the logistic model (LM) to develop a dynamic model of A. fumigatus branching for the prediction of the specific growth rate of branching value (0.23 h-1). CONCLUSIONS: Developed FAMI and LM models present a simple and non-destructive method of predicting the evolution of branching complexity of A. fumigatus. These models are useful as laboratory measurements for the prediction of hyphal and mycelium development, especially relevant to the pathogenesis study of aspergillosis, as well as pathogenesis of other diseases caused by moulds.

Size and Shape Filtering of Malignant Cell Clusters within Breast Tumors Identifies Scattered Individual Epithelial Cells as the Most Valuable Histomorphological Clue in the Prognosis of Distant Metastasis Risk.

Survival and life quality of breast cancer patients could be improved by more aggressive chemotherapy for those at high metastasis risk and less intense treatments for low-risk patients. Such personalized treatment cannot be currently achieved due to the insufficient reliability of metastasis risk prognosis. The purpose of this study was therefore, to identify novel histopathological prognostic markers of metastasis risk through exhaustive computational image analysis of 80 size and shape subsets of epithelial clusters in breast tumors. The group of 102 patients had a follow-up median of 12.3 years, without lymph node spread and systemic treatments. Epithelial cells were stained by the AE1/AE3 pan-cytokeratin antibody cocktail. The size and shape subsets of the stained epithelial cell clusters were defined in each image by use of the circularity and size filters and analyzed for prognostic performance. Epithelial areas with the optimal prognostic performance were uniformly small and round and could be recognized as individual epithelial cells scattered in tumor stroma. Their count achieved an area under the receiver operating characteristic curve (AUC) of 0.82, total area (AUC = 0.77), average size (AUC = 0.63), and circularity (AUC = 0.62). In conclusion, by use of computational image analysis as a hypothesis-free discovery tool, this study reveals the histomorphological marker with a high prognostic value that is simple and therefore easy to quantify by visual microscopy.

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.

Investigating the Fractal Dimension of the Foveal Microvasculature in Relation to the Morphology of the Foveal Avascular Zone and to the Macular Circulation in Patients With Type 2 Diabetes Mellitus.

In this study, we examined the relationship between the fractal dimension (FD), the morphology of the foveal avascular zone (FAZ) and the macular circulation in healthy controls and patients with type 2 diabetes mellitus (T2DM) with and with no diabetic retinopathy (DR). Cross-sectional data of 47 subjects were analyzed from a 5-year longitudinal study using a multimodal optical imaging approach. Healthy eyes from nondiabetic volunteers (n = 12) were selected as controls. Eyes from patients with T2DM were selected and divided into two groups: diabetic subjects with mild DR (MDR group, n = 15) and subjects with DM but without DR (DM group, n = 20). Our results demonstrated a higher FD in the healthy group (mean, 1.42 ± 0.03) than in the DM and MDR groups (1.39 ± 0.02 and 1.35 ± 0.03, respectively). Also, a bigger perimeter, area, and roundness of the FAZ were found in MDR eyes. A significant difference in area and perimeter (p ≤ 0.005) was observed for the MDR group supporting the enlargement of the FAZ due to diabetic complications in the eye. A moderate positive correlation (p = 0.014, R2 = 43.8%) between the FD and blood flow rate (BFR) was only found in the healthy control group. The BFR calculations revealed the lowest values in the MDR group (0.98 ± 0.27 µl/s vs. 1.36 ± 0.86 µl/s and 1.36 ± 0.57 µl/sec in the MDR, DM, and healthy groups, respectively, p = 0.2). Our study suggests that the FD of the foveal vessel arborization could provide useful information to identify early morphological changes in the retina of patients with T2DM. Our results also indicate that the enlargement and asymmetry of the FAZ might be related to a lower BFR because of the DR onset and progression. Interestingly, due to the lack of FAZ symmetry observed in the DM and MDR eyes, it appears that the distribution of flow within the retinal vessels loses complexity as the vascular structures distributing the flow are not well described by fractal branching. Further research could determine how our approach may be used to aid the diagnosis of retinal neurodegeneration and vascular impairment at the early stage of DR.

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. Data obtained using Sholl's method is not always subjected to complete statistical analysis. The problem becomes particularly apparent in the quantitative examination of dendritic structures. Our aim was also to perform a careful analysis of our data for normality, in order to choose the appropriate statistical method for data processing. In the linear Sholl analysis, it is important to properly represent and interpret the frequency functions. The objective of this study was also to investigate the problems of determining the frequency functions, plotting the corresponding lines of regression, and measuring the degree of fluctuation of experimental data points around these lines. The main result of our testing is a confirmation of Rexed's laminar scheme: we have proved that there are 6 out of 10 possible pairs of samples where one member significantly differs from the other, i.e. one lamina is significantly distinguishable from the other.