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. 2015 Sep 2;10:151. doi: 10.1186/s13000-015-0383-0

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© Weis et al. 2015

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

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Fig. 1 — Illustration of the task and the solution via a RBF. a: Sketch of two serial sections where a single lymphocyte in the centre could be appreciated in both sections. (A1) One task is to colocalize this cell/its immunohistochemical staining in both sections. (A2) Another task is to measure its distance to the bone trabeculae. (A3) Furthermore, is should be allocated to niches via measuring its distance to certain objects (bone trabeculae, other cells, vessels). b: By usage of different parameters (β and γ in equation 1) a RBF for direct and indirect spatial interaction could be modelled according to the particular image resolution/pixel-distance relation. The parameters are here chosen to accomplish a shape for RBF_direct, which represents potential direct object-object interaction, and for RBF_indirect, which represents paracrine interaction. Black solid line: One point at position x_p = 0 (representing a nucleus) is convoluted with an inverse, multiquadric basis function for direct interaction (RBF_direct with β = 3 and γ = 0.01). For illustration purposes the RBF is only shown with one variable. As a consequence, every point in this figure (xЄ [−100,800]) has an arbitrary scalar field value [arbitrary density]. Blue dashed line: Overlay of two fields for direct interaction, where one represents a centroid at x_p = −50 and one at x_p = 50.Red solid line: The single point at position x_p = 0 is convoluted with an inverse, multiquadric basis function for indirect interaction (RBF_indirect with β = 3 and γ = 0.00002)