Germinal center analysis with the tools of mathematical morphology on graphs

Only few studies devoted to quantitative analysis of tissue architecture have been performed. The analysis of neighborhood relationships between cells, using graphs and mathematical morphology (MM), constitutes one approach. We propose to analyse quantitatively the architecture of a tissue with the tools of MM on graphs. The use of graphs seems best suited to take into account the neighborhood relationships between cells, independently from their mutual distances: two cells are considered as neighbors if no interfering cell is placed in a given sense between them. Such neighboring cells are linked by an arc in a graph. On such a graph, all tools of MM may be applied. We investigate two of them in the present work: (1) the distance transforms permits to analyse the repartition of a cellular population A relative to population B, (2) the size distribution permits to analyse the tendancy of a cell population to form clusters. We have applied this method using Gabriel's graph, derived from the Voronoï diagram, to determine the "zone of influence" of a cell. We have analysed the neighborhood relationships between cells in germinal centers (GC) from lymph nodes. Twelve hyperplastic GCs from follicular hyperplasia (FH) and 5 neoplastic GCs from small cleaved cell follicular lymphoma (++SCCFL) have been studied; 2 microns hematoxylin-eosin plastic embedded sections have been analysed. Cell nuclei have been identified manually by the observer by giving a numerical and image color code. Gabriel's graphs have been constructed with all centrofollicular cells. Subgraphs with only lymphoid cells, large cells or small cleaved cells have also been studied. The application of MM transformations on the graphs using software package Morphograph has allowed a quantitative description of cell distribution in the tissue. The distances of centrofollicular lymphoid cells from the periphery of the GCs (mantle zone), from nonlymphoid cells as macrophages located within the GCs and between large lymphoid cells and small lymphoid cells have been determined in FH and SCCFL. Using iterative closings and openings, we have detected aggregates of small and large cells and characterized their size and distribution in the GCs. The application of this method on lymph node biopsy has allowed a quantitative description and comparison of GCs in different pathological conditions.