Physics approaches to the spatial distribution of immune cells in tumors

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.