Fractal dimension, occupancy and hotspot analyses of B cell spatial distribution predict clinical outcome in breast cancer

While the density of tumor-infiltrating lymphocytes (TILs) is now well known to correlate with clinical outcome, the clinical significance of spatial distribution of TILs is not well characterized. We have developed novel statistical techniques (including fractal dimension differences, a hotspot analysis, a box counting method that we call ‘occupancy’ and a way to normalize cell density that we call ‘thinning’) to analyze the spatial distribution (at different length scales) of various types of TILs in triple negative breast tumors. Consistent with prior reports, the density of CD20 B cells within tumors is not correlated with clinical outcome. However, we found that their spatial distribution differs significantly between good clinical outcome (no recurrence within at least 5 years of diagnosis) and poor clinical outcome (recurrence with 3 years of diagnosis). Furthermore, CD20 B cells are more spatially dispersed in good outcome tumors and are more likely to infiltrate into cancer cell islands. Lastly, we found significant correlation between the spatial distributions of CD20 B cells and CD8 (cytotoxic) T cells (as well as CD3 T cells), regardless of outcome. These results highlight the significance of the spatial distribution of TILs, especially B cells, within tumors.