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In the present study, 53 cases of squamous cell carcinomas of the head and neck were characterized by a quantitative histological texture analysis based on principles of spatial statistics. A planar tessellation of the epithelial tumour component was generated by a skeletonization algorithm. The size distribution of the virtual cells of this planar tessellation, and the size distribution of the profiles of the tumour cell nuclei were estimated in terms of area and boundary length. The intensity, the reduced second moment function (K-function) and the pair correlation function of the point process of the centroids of the profiles of the tumour cell nuclei were also estimated. For both purposes, it is necessary to correct for edge effects, which we consider in this paper in some detail. Specifically, the point patterns of the tumour cell nuclei were considered as realizations of a point process, where the points exist only in the epithelial tumour component (the permitted phase) and not in the stroma (the forbidden phase). The methods allow to characterize each individual tumour by a series of summary statistics. The total set of cases was then partitioned into two groups: 19 cases without lymph node metastases (pN0), and 34 nodal positive cases (pN1 or pN2). Statistical analysis showed no significant differences between the intensities, the mean K-functions and the mean pair correlation functions of the tumour cell nucleus profiles of the two groups. However, there were some significant differences between the sizes of the virtual cells and of the nucleus profiles of the nodal negative cases as compared to the nodal positive cases. In a logistic regression analysis, one of the quantitative nuclear size variables (mean nuclear area) was found to be a significant predictor of lymph node metastasis, in addition to tumour stage. The study shows the potential of methods of spatial statistics for objective quantitative grading of squamous cell carcinomas of the head and neck, and provides an example for modelling histological point patterns as realizations of planar point processes occupying a reference phase which is only a partial component of the total tissue.

This paper deals with the estimation of the intensity of a planar point process on the basis of a single point pattern, observed in a rectangular window. If the model assumptions of stationarity and isotropy hold, the method of block bootstrapping can be used to estimate the intensity of the process with confidence bounds. The results of two variants of block bootstrapping are compared with a parametric approximation based on the assumption of a Gaussian distribution of the numbers of points in deterministic subwindows of the original pattern. The studies were performed on patterns obtained by simulation of well-known point process models (Poisson process, two Matern cluster processes, Matern hardcore process, Strauss hardcore process). They were also performed on real histopathological data (point patterns of capillary profiles of 12 cases of prostatic cancer). The methods are presented as worked examples on two cases, where we illustrate their use as a check on stationarity (homogeneity) of a point process with respect to different fields of vision. The paper concludes with various methodological discussions and suggests possible extensions of the block bootstrap approach to other fields of spatial statistics.

Summary In this study, we quantitatively investigate the role of the M97 protein for viral morphogenesis in murine cytomegalovirus (MCMV)-infected fibroblast cells. For this purpose, a statistical analysis is performed for the spatial distribution of nuclear B-capsids (devoid of DNA, containing the scaffold) and C-capsids (filled with DNA). Cell nuclei infected with either wild-type or an M97 deletion mutant were compared. Univariate and multivariate point process characteristics (like Ripley's K-function, the L-function and the nearest neighbour distance distribution function) are investigated in order to describe and quantify the effects that the deletion of M97 causes to the process of DNA packaging into nucleocapsids. The estimation of the function L(r) −r reveals that with respect to the wild type there is an increased frequency of point pairs at a very short distance (less than approximately 100 nm) for both the B-capsids as well as for the C-capsids. For the M97 deletion mutant type this is no longer true. Here only the C-capsids show such a clustering behaviour, whereas for B-capsids it is almost nonexistant. Estimations of functionals such as the nearest neighbour distance distribution function confirmed these results. Thereby, a quantification is provided for the effect that the deletion of M97 leads to a loss of typical nucleocapsid clustering in MCMV-infected nuclei.

The keratin filament network is an important part of the cytoskeleton. It is involved in the regulation of shape and viscoelasticity of epithelial cells. The morphology of keratin networks depends on post-translational modifications of keratin monomers. In-vitro studies indicated that network characteristics, such as filament crosslink density, determines the biophysical properties of the filament network. This report presents a quantitative method for the morphological analysis of keratin filament networks. Visualization of filaments was based on prefixation extraction of epithelial cells and scanning electron microscopy (SEM). SEM images were processed by a skeletonization algorithm to obtain a graph structure that represents individual filaments as well as their connections. This method was applied to investigate the effects of transforming growth factor alpha (TGFalpha) on the morphology of keratin networks in pancreatic cancer cells. TGFalpha contributes to pancreatic cancer progression and activates signalling pathways phosphorylating keratin monomers. Using this new method, a significant alteration to the keratin network morphology could be detected in response to TGFalpha.

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 gamma 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.

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.

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.

We suggest the use of bootstrap methods for inference from stereological estimates of volume fraction. An informal introduction to stereological estimation of volume fraction and to principles of bootstrap techniques is given. The bootstrap method is a robust computer-intensive resampling technique, based on independent random sampling from a data set with replacement. Bootstrap methods were used to estimate confidence intervals for volume fractions, and to test for a significant difference between estimated volume fractions from two samples. Two sampling designs are considered: independent replicated samples (visual fields) from a single object, and estimates of volume fraction from multiple independent objects. The methods are presented as worked examples on real data sets obtained from tumour pathology (mammary cancer, pancreatic cancer). The volume fraction of glandular lumina per total volume of the epithelial phase was chosen as target parameter. It indicates the degree of glandular differentiation in adenocarcinomas and is estimated as a ratio-of-means statistic with variable denominator within cases. The confidence intervals of the volume fraction estimated by the bootstrap method were slightly narrower than the parametrically calculated confidence intervals for all data sets. The outcomes of significance tests based on the bootstrap technique were unchanged as compared with classical tests based on the assumptions of normality and homoscedasticity of the data. Special attention was paid to the reproducibility of the bootstrap technique in replicated trials on the same data.

Translocation of genes into the pericentromeric heterochromatin occurs during cellular differentiation and leads to a long-term silencing of these genes. Consequently, a structural remodelling of this heterochromatin compartment is observed during differentiation but this remains to be defined from a topological point of view. In a previous study, we analysed the three-dimensional (3D) distribution patterns of centromere clusters (chromocentres) by confocal scanning laser microscopy and found that differentiation of the promyelocytic leukaemia cell line NB4 along the neutrophil lineage is associated with a progressive clustering of centromeres. This clustering was reflected by a decreased number of detectable chromocentres, i.e. groups of centromeres with a distance below the diffraction-limited resolution of optical microscopy. The purpose of this study was to perform a statistical analysis of the 3D distribution of chromocentres in NB4 cells. Several point field characteristics (Ripley's K-function, L-function, pair correlation function, nearest-neighbour distribution function) were investigated to describe the topology of chromocentres during differentiation of NB4 cells. The pair correlation function revealed a higher frequency of chromocentre distances between 350 nm and 800 nm in undifferentiated NB4 cells as compared with differentiated cells. The L-function and the nearest-neighbour distribution function confirmed these results. These data imply the existence of intranuclear heterochromatin zones formed by functionally related centromeric regions. In view of the observed decrease in the number of detectable chromocentres during differentiation, we hypothesize that these zones with a diameter of 350-800 nm in undifferentiated NB4 cells contract into zones with a diameter below 350 nm in differentiated cells.