FunSpace: A functional and spatial analytic approach to cell imaging data using entropy measures

Spatial heterogeneity in the tumor microenvironment (TME) plays a critical role in gaining insights into tumor development and progression. Conventional metrics typically capture the spatial differential between TME cellular architectures by either exploring the cell distributions in a pairwise fashion or aggregating the heterogeneity across multiple cell distributions without considering for the spatial contribution. As such, none of the existing approaches has fully accounted for the heterogeneity caused by both cellular diversity and spatial configurations of multiple cell categories. In this article, we propose an approach to leverage the spatial entropy measures at multiple distance ranges to account for the spatial heterogeneity across different cellular architectures. Then, functional principal component analysis (FPCA) targeting sparse data is applied to estimate FPC scores which are then predictors in a Cox regression model to investigate the impact of spatial heterogeneity in the TME on survival outcome, holding other clinical variables constant. Using an ovarian cancer dataset (n = 114) as a case study, we found that the spatial heterogeneity in the TME immune compositions of CD19+ B cells, CD4+ T cells, CD8+ T cells, and CD68+ macrophages, had a significant non-zero effect on the overall survival (p = 0.027). In the simulations studies under different spatial configurations, the proposed method demonstrated a high predictive power by accounting for both clinical effect and the impact of spatial heterogeneity. ### Competing Interest Statement The authors have declared no competing interest.