On the spatial statistics of the cytoskeleton

The three dimensional structure of the different types of cytoskeletal filaments (CSK) consti¬ tutes the cell's shape as well as die interior organization of cell organelles. Since changes in the state of cells towards neoplastic transformations are known to affect the morphology of the cell it can be assumed that these deformations can be quantitatively described by means of the cytoskel¬ eton. Thus the investigation of the structural organization of the cytoskeletal meshwork appears as a promising approach to develop new quantitative methods for histopathology. The development of the confocal laser scanning microscopes (CLSM), which we experienced in the eighties from merely a concept to a versatile and powerful tool in science and in daily prac¬ tical use, togemer with the availability of specific antibody markers for the CSK proteins, opened up the way for the analysis of the 3-D structure of this interesting cell constituent. Besides the three dimensional resolution of the CLSM, the choice of (fluorescence) light microscopy for this study provided a considerably easier and faster process of preparation of the cells as it is possible for electron microscopy. The complex meshwork of the cytoskeleton reveals a wide variety of patterns, demanding an appropriate description to cover its genuine properties for a quantitative analysis. In this work we consider the analysis of the CSK based on two hypotheses: I The unique structural qualities of the cytoskeletal meshwork are most adequately represented in terms of a planar and undirected graph. II The statistical properties of the cytoskeletal meshwork can be evaluated by modelling the CSK graph with spatial point and area processes. In the first part we present the techniques for die image processing of the raw CLSM slices and introduce a new filtering method based on connectionist feedforward networks, as well as an adaptive pattern recognition algoridim for the binarization. The relevant image content is represented in terms of graph theory. The statistical properties of the graphs are evaluated based on a hypothesis testing approach. We present the methods of spatial statistics for the analysis of the distribution of the vertices and the edges. Furthermore we introduce a new test on the cycle basis of the CSK graph, which proves to be more sensitive to regular and periodic structures than the tests from spatial statistics. The CSK meshwork is modelled by spatial point and area processes with varying underlying assumptions about the pattern generating process. Transformations from point to area processes and vice versa allow us to interchangeably apply the appropriate tests in their relevant domain. The usability of die unique structural properties of the cytoskeleton meshwork for classifica¬ tion purposes requires die content of significant information. Consequently, the case study on die given data focuses on me test on complete spatial randomness. The detailed investigation of the few data sets available revealed no evidence for a significant deviation of the CSK structures from a random pattern generation process. However, the methodology developed here proved