Graph-Based Approach for Spatial Heterogeneity Analysis in Tumor Microenvironment
The interaction between tumor and surrounding microenvironment (TME) is recognized as playing
an important role in the progression of the disease. Understanding of the interaction between tumor and
immune system is the focus of several studies dedicated to the improvement of cancer immunotherapy
effectiveness . On the other hand, it has been shown that invasion and metastasis of breast tumors is influenced by collagen organization at the tumor-stromal interface . The characterization of such interactions relies on an efficient spatial distribution quantification of TME. Graph-based analysis tools are the best suitable to answer this question as they have the ability to represent spatial arrangements and neighborhood relationships of different tissue components .
In this work, we propose a novel approach to characterize the spatial relationships between cancer cells and TME components in breast tumors, using graph theory and sparse sets’ mathematical morphology (MM). The tools of morphology on graphs were first used in  to study the neighborhood relationships between cells in germinal centers from lymph nodes, then in  for semantic spatial configuration modeling in histopathology. In our study, we propose new morphological descriptors characterizing the tumor architecture and the interactions with TME cells.
Towards a better evaluation and understanding, we use simulated data of different breast tumor types , , where locations of cancer nuclei (CN), fibroblasts (synthesizers of collagen, FN), and lymphocytes (LN) are already known. In order to set neighborhood relationships between different cells, Delaunay graph  is first reconstructed on all cells, and alpha-shape filter  is applied to circumvent border effects, giving new graph denoted G . The designed features are extracted basically from two different morphological operations. The first operation is composed of successive morphological erosions  applied to the subgraph induced by CN (denoted SGC, ), repeated until the subgraph is null. The curve given by the number of CN in terms of erosions provides 3 significant characteristics : I) The origin slope describes the number of CN on the boundary of tumor aggregates (TA) and, thus, the tumor-stromal interface ; II) The area under curve (AUC) reflects the density within TAs, and III) the number of iterations outlines the morphologic radius of the largest TA and, consequently, the geodesic distance of the farthest tumor cell from LN and/or FN. The second morphological operation is composed of successive morphological dilations applied to SGC with non-overlapping control of labeled connected-components . The goal behind this operation is to investigate the TME cells surrounding each TA. The ratio between the number of LN and the number of CN, and the means of the Euclidean and the geodesic distances of LN from CN on the boundary are calculated for each TA .
In this work, we have briefly presented a conceptual framework for analyzing the architecture of breast
tumors and the interactions with the surrounding microenvironment. New graph-based features were
proposed to characterize the spatial distribution of TME components and were tested on simulated data. In our future works, we will include adipose tissue , blood vessels and endothelial cells. We will also focus on the anisotropic characterization of collagen, and test the approach on real dataset.
 M. W. Conklin, J.C. Eickhoff, K. M. Riching, C. A. Pehlke, K. W. Eliceiri, P.P. Provenzano, A. Friedl, P. J. Keely , Aligned Collagen Is a Prognostic Signature for Survival in Human Breast Carcinoma, Am J Pathol. 2011, 178(3):1221-32.
 H. Sharma, N. Zerbe, S. Lohmann, K. Kayser, O. Hellwich, P. Hufnagl , A review of graph-based methods for image analysis in digital histopathology 2015,1:61
 E. Raymond, M. Raphael, M. Grimaud, L. Vincent, J. L. Binet, F. Mayer , Germinal center mathematical analysis with the tools of morphology on graphs, Cytometry. 1993, 14(8):848-61.
 N. Loménie, D. Racoceanu, Point Set Morphological Filtering and Semantic Spatial Configuration Modeling: application to microscopic image and biostructure analysis, Pattern Recognition 2012, 8(45): 2894–2911.
 M. Wagner, R. Bjerkvig, H. Wiig, J. M. Melero-Martin , R-Z. Lin, M. Klagsbrun, A.C. Dudley, Inflamed tumor-associated adipose tissue is a depot for macrophages that stimulate tumor growth and angiogenesis, Angiogenesis. 2012, 15(3):481-95.
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