Occupancy and fractal dimension analyses of the spatial distribution of cytotoxic (CD8+) T cells infiltrating the tumor microenvironment in triple negative breast cancer

Favorable outcomes have been associated with high densities of tumor infiltrating lymphocytes (TILs) such as cytotoxic (CD8+) T cells. However, the clinical signifi- cance of the spatial distribution of TILs is less well understood. We have developed novel statistical techniques to characterize the spatial distribution of TILs at various length scales. These include a box counting method that we call “occupancy” and novel applications of fractal dimensions. We apply these techniques to the spatial distribution of CD8+ T cells in the tumor microenvironment of tissue resected from 35 triple negative breast cancer patients. We find that there is a distinct difference in the spatial distribution of CD8+ T cells between good clinical outcome (no recurrence within at least 5 years of diagnosis) and poor clinical outcome (recurrence within 3 years of diagnosis). The statistical significance of the difference between good and poor outcome in the occupancy, fractal dimension (FD), and FD difference of CD8+ T cells is comparable to that of the CD8+ T cell density. Even when we randomly exclude some of the cells so that the images have the same cell density, we still find that the fractal dimension at short length scales is correlated with cancer recurrence, implying that the actual spatial distribution of CD8+ cells, and not just the CD8+ cell density, is associated with clinical outcome. The occupancy and FD difference indicate that the CD8+ T cells are more spatially dispersed in good outcome and more aggregated in poor outcome. We discuss possible interpretations