Spatial Analysis of Malignant-Immune Cell Interactions in the Tumor Microenvironment Using Topological Data Analysis

The spatial interactions between malignant and immune cells in the tumor microenvironment (TME) play a crucial role in cancer biology and treatment response. Understanding these interactions is critical for predicting prognosis and assessing immunotherapy effectiveness. Conventional methods, which focus on local spatial features, often struggle to achieve robust analysis due to the complex and heterogeneous cellular distributions. We propose a Topological Data Analysis (TDA)-based framework using both global and local spatial features between malignant and immune cells. For the global aspects, we introduce Topological Malignant Clusters (TopMC), a method utilizing persistence diagrams in TDA to capture the global spatial shapes of malignant cell distributions. It quantifies tumor-immune cell infiltration at a global scale by computing distances from the boundaries of the TopMC. Local interactions are evaluated through the density of malignant cells. Using high-resolution multiplex immunofluorescence (mIF) imaging in Diffuse Large B Cell Lymphoma, we integrate distance and density measures into a distance-density space to analyze patterns of malignant-immune cell interactions in TME. This study shows the robustness of the proposed approach to variations in cell distribution, enabling consistent analysis irrespective of whether images are acquired from malignant-enriched or border regions of the tumors. Furthermore, we elucidate the correlation between spatial patterns of immune phenotypes and patient survival probability.