The goal of immunotherapy is to mobilize the immune system to kill cancer cells. Immunotherapy is more effective and, in general, the prognosis is better, when more immune cells infiltrate the tumor. We explore the question of whether the spatial distribution rather than just the density of immune cells in the tumor is important in forecasting whether cancer recurs. After reviewing previous work on this issue, we introduce a novel application of maximum entropy to quantify the spatial distribution of discrete point-like objects. We apply our approach to B and T cells in images of tumor tissue taken from triple negative breast cancer patients. We find that the immune cells are more spatially dispersed in good clinical outcome (no recurrence of cancer within at least 5 years of diagnosis) compared to poor clinical outcome (recurrence within 3 years of diagnosis). Our results highlight the importance of spatial distribution of immune cells within tumors with regard to clinical outcome, and raise new questions on their role in cancer recurrence.

While tumor infiltration by CD8⁺ T cells is now widely accepted to predict outcomes, the clinical significance of intratumoral B cells is less clear. We hypothesized that spatial distribution rather than density of B cells within tumors may provide prognostic significance. We developed statistical techniques (fractal dimension differences and a box-counting method 'occupancy') to analyze the spatial distribution of tumor-infiltrating lymphocytes (TILs) in human triple-negative breast cancer (TNBC). Our results indicate that B cells in good outcome tumors (no recurrence within 5 years) are spatially dispersed, while B cells in poor outcome tumors (recurrence within 3 years) are more confined. While most TILs are located within the stroma, increased numbers of spatially dispersed lymphocytes within cancer cell islands are associated with a good prognosis. B cells and T cells often form lymphocyte clusters (LCs) identified via density-based clustering. LCs consist either of T cells only or heterotypic mixtures of B and T cells. Pure B cell LCs were negligible in number. Compared to tertiary lymphoid structures (TLS), LCs have fewer lymphocytes at lower densities. Both types of LCs are more abundant and more spatially dispersed in good outcomes compared to poor outcome tumors. Heterotypic LCs in good outcome tumors are smaller and more numerous compared to poor outcome. Heterotypic LCs are also closer to cancer islands in a good outcome, with LC size decreasing as they get closer to cancer cell islands. These results illuminate the significance of the spatial distribution of B cells and LCs within tumors.