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 threedimensional 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.

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 S100beta-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.

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SummaryIn 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.

No abstract