Stefanie Eckel

Spatial Arrangement of Microglia in the Mouse Hippocampus: A Stereological Study in Comparison with Astrocytes

Microglia are classically considered to be immune cells in the brain, but have now been proven to be involved in neuronal activity as well. Here we stereologically analyzed the spatial arrangement of microglia in the mouse hippocampus. First, we estimated the numerical densities (NDs) of microglia identified by ionized calcium‐binding adaptor molecule 1 (Iba1). Despite that microglia appeared to be evenly distributed throughout the hippocampal area, the NDs demonstrated significant dorsoventral, interregional, and interlaminar differences. Briefly, the NDs in the ventral hippocampus were significantly lower in the CA3 region than in the CA1 region and dentate gyrus, although no interregional differences were detectable in the dorsal hippocampus. Both in the CA1 and CA3 regions, the NDs were significantly higher in the stratum lacunosum‐moleculare than in the remaining layers. Next, we investigated the spatial patterns of distribution of Iba1‐labeled microglia and S100β‐labeled astrocytes. So far as we examined, the somato–somatic contacts were not seen among microglia or among astrocytes, whereas the close apposition between microglia and astrocytes were occasionally detected. The 3D point process analysis showed that the spatial distribution of microglia was significantly repulsive. Because the statistical territory of single microglia was larger than that estimated from process tracing, they are not likely to touch each other with their processes. Astrocytes were distributed slightly repulsively with overlapping areas. The 3D point process analysis also revealed a significant spatial attraction between microglia and astrocytes. The present findings provide a novel anatomical basis for glial research.

Statistical analysis of reduced pair correlation functions of capillaries in the prostate gland

Blood capillaries are thread‐like structures that may be considered as an example of a spatial fibre process in three dimensions. At light microscopy, the capillary profiles appear as a planar point process on sections. It has recently been shown that the observed pair correlation function g(r) of the centres of the fibre profiles on two‐dimensional sections may be used to estimate the reduced pair correlation function of stationary and isotropic fibre processes in three dimensions. In the present study, we explored how this approach may be extended to statistical analysis of reduced g‐functions of capillaries from multiple specimens of different groups and with replicated observations. The methods were applied to normal prostatic tissue compared with prostate cancer. Confidence intervals for the mean reduced g‐functions of groups were estimated for fixed r‐values parametrically using the t‐distribution, and by bootstrap methods. Each estimated reduced g‐function was furthermore characterized in terms of its first maximum and minimum. The mean length of capillaries per unit tissue volume was significantly higher in prostate cancer tissue than in normal prostate tissue. Significant differences between the mean reduced g‐functions of malignant and benign lesions could be demonstrated for two domains of r‐values. In general, bootstrap‐based confidence intervals were slightly wider than parametrically estimated confidence intervals. Falsely negative lower bounds of the intervals, which sometimes arose using the parametric approach, could be avoided by the bootstrap method. Testing of group mean values for significant differences by the bootstrap method yielded more conservative results than multiple t‐tests. The functional value of the first maximum of the reduced g‐function and a global statistical parameter of short‐range ordering was significantly reduced in the carcinoma group. Prostate cancer tissue is more densely supplied with capillaries than normal prostate tissue and the three‐dimensional arrangement of the vessels differs with respect to interaction at various distance ranges. In the local approach used here, bootstrap methods can be used as a robust statistical tool for the computation of confidence intervals and group comparisons of mean reduced g‐functions at specific ranges of interaction.

Actin network architecture and elasticity in lamellipodia of melanoma cells

Cell migration is an essential element in the immune response on the one hand and in cancer metastasis on the other hand. The architecture of the actin network in lamellipodia determines the elasticity of the leading edge and contributes to the regulation of migration. We have implemented a new method for the analysis of actin network morphology in the lamellipodia of B16F1 mouse melanoma cells. This method is based on fitting multi-layer geometrical models to electron microscopy images of lamellipodial actin networks. The chosen model and F-actin concentrations are thereby deterministic parameters. Using this approach, we identified distinct structural features of actin networks in lamellipodia. The mesh size which defines the elasticity of the lamellipodium was determined as 34 and 78?nm for a two-layer network at a total actin concentration of 9.6?mg?ml?1. These data lead to estimates of the low frequency elastic shear moduli which differ by more than a magnitude between the two layers. These findings indicate an anisotropic shear modulus of the lamellipodium with the stiffer layer being the dominant structure against deformations in the lamellipodial plane and the softer layer contributing significantly at lower indentations perpendicular to the lamellipodial plane. This combination creates a material that is optimal for pushing forward as well as squeezing through narrow spaces.

Statistical modelling of the geometry of planar sections of prostatic capillaries on the basis of stationary Strauss hard-core processes

In a recent study, the capillarization of normal prostatic tissue and prostatic carcinoma tissue was characterized by means of explorative methods of spatial statistics. In the present paper, an attempt was made to go beyond the explorative approach and to characterize the observed point patterns of the capillary profiles on sections by means of a parametric model. For this purpose, the flexible class of Gibbs processes was considered. Specifically, stationary Strauss hard‐core processes were fitted to the observed point patterns. The goodness of fit achieved by the model was checked by simulations with the Markov chain Monte Carlo method using the Metropolis–Hastings algorithm. Model fitting and simulations were performed with the help of the spatstat package under R. The observed point patterns were in some cases compatible with realizations of stationary Strauss hard‐core processes for all ranges of spatial interaction. However, deviations from the model were found for one or more domains of ranges in other cases. In the tumour tissue, a highly significant decrease of the interaction parameter of the Strauss hard‐core process could be found as compared to the normal prostatic tissue. This finding is discussed in terms of a loss of the normal lobular architecture of the glands in the tumour tissue.

Statistical analysis of labelling patterns of mammary carcinoma cell nuclei on histological sections

It is of central interest for tumour biology to explore the mechanisms of tumour cell proliferation. In this study, methods of spatial statistics were used to study the spatial distribution of proliferating cells within tumour tissue quantitatively and objectively. Mammary cancer tissue was studied as an example. It was attempted to clarify whether cell division occurs entirely at random (random labelling), i.e. the process of division occurs at random, independently from the state of the neighbouring nuclei, or whether the spatial distribution of proliferation is more complex, e.g. in the form of actively proliferating clusters alternating with relatively silent zones. In the case of random labelling, the reduced second moment functions K(r) of the labelled and the unlabelled nuclei would be identical. The same would hold for the pair correlation functions g(r). The alternative hypothesis is that the second‐order properties of the processes of the labelled and the unlabelled nuclei are different. Twenty cases of invasive ductal mammary carcinomas were studied. The nuclei of proliferating cells were stained immunohistochemically with the monoclonal antibody MIB‐1, which detects specifically the proliferation‐associated nuclear antigen Ki 67. The planar coordinates of the tumor cell nucleus profiles from two rectangular visual fields per case were recorded. For each visual field, the following investigations were performed: estimation of the explorative summary characteristics K(r) and g(r), fitting of the parameters of a stationary Strauss hard‐core model to the observed point patterns, estimation of two distance‐dependent Simpson indices and Monte Carlo tests of all individual patterns on the null hypothesis of random labelling. Significant differences between the mean K‐functions and the mean g‐functions of the labelled and the unlabelled nuclei were found. Moreover, the mean interaction parameter γ of the stationary Strauss hard‐core model was significantly higher for the labelled nuclei than for the unlabelled nuclei. The estimates of the two distance‐dependent Simpson indices showed a tendency of points with the same label towards a positive spatial correlation. In the Monte Carlo tests, the null hypothesis of random labelling was rejected for the majority of the visual fields. These four lines of investigation led to the concordant conclusion that the labelling of mammary carcinoma nuclei by MIB‐1 is not simply random. The data suggest that the second‐order properties of the point process of the labelled nuclei are significantly different from those of the unlabelled nuclei. In particular, the process of the labelled nuclei shows a higher degree of clustering (increased strength of interaction) than the process of the unlabelled points.

Modelling Tree Roots in Mixed Forest Stands by Inhomogeneous Marked Gibbs Point Processes

The aim of the paper is to apply point processes to root data modelling. We propose a new approach to parametric inference when the data are inhomogeneous replicated marked point patterns. We generalize Geyers saturation point process to a model, which combines inhomogeneity, marks and interaction between the marked points. Furthermore, the inhomogeneity influences the definition of the neighbourhood of points. Using the maximum pseudolikelihood method, this model is then fitted to root data from mixed stands of Norway spruce (Picea abies (L.) Karst.) and European beech (Fagus sylvatica L.) to quantify the degree of root aggregation in such mixed stands. According to the analysis there is no evidence that the two root systems are not independent.