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Background  Immunohistochemical analysis of cellular interactions in the bone marrow in situ is demanding, due to its heterogeneous cellular composition, the poor delineation and overlap of functional compartments and highly complex immunophenotypes of several cell populations (e.g. regulatory T-cells) that require immunohistochemical marker sets for unambiguous characterization. To overcome these difficulties, we herein present an approach to describe objects (e.g. cells, bone trabeculae) by a scalar field that can be propagated through registered images of serial histological sections.    Methods  The transformation of objects within images (e.g. cells) to a scalar field was performed by convolution of the object’s centroids with differently formed radial basis function (e.g. for direct or indirect spatial interaction). On the basis of such a scalar field, a summation field described distributed objects within an image.    Results  After image registration i) colocalization analysis could be performed on basis scalar field, which is propagated through registered images, and - due to the shape of the field – were barely prone to matching errors and morphological changes by different cutting levels; ii) furthermore, depending on the field shape the colocalization measurements could also quantify spatial interaction (e.g. direct or paracrine cellular contact); ii) the field-overlap, which represents the spatial distance, of different objects (e.g. two cells) could be calculated by the histogram intersection.    Conclusions  The description of objects (e.g. cells, cell clusters, bone trabeculae etc.) as a field offers several possibilities: First, co-localization of different markers (e.g. by immunohistochemical staining) in serial sections can be performed in an automatic, objective and quantifiable way. In contrast to multicolour staining (e.g. 10-colour immunofluorescence) the financial and technical requirements are fairly minor. Second, the approach allows searching for different types of spatial interactions (e.g. direct and indirect cellular interaction) between objects by taking field shape into account (e.g. thin vs. broad). Third, by describing spatially distributed groups of objects as summation field, it gives cluster definition that relies rather on the bare object distance than on the modelled spatial cellular interaction.    Electronic supplementary material  The online version of this article (doi:10.1186/s13000-015-0383-0) contains supplementary material, which is available to authorized users.

diagnostic pathology

On the representation of cells in bone marrow pathology by a scalar field: propagation through serial sections, co-localization and spatial interaction analysis