Breast Cancer Reaction-Diffusion from Spectral-Spatial Analysis in Immunohistochemistry

Cancer is a prevalent disease, and while many significant advances have been made, the ability to accurately predict how an individual tumor will grow – and ultimately respond to therapy – remains limited. We use spatial-spectral analysis of 20 patients accrued to a phase II study of preoperative SABR with 9.5 × 3 Gy for early-stage breast cancer whose tissues were stained with multiplex immunofluorescence. We employ the reaction-diffusion framework to compare the data-deduced two-point correlation function and the corresponding spatial power spectral distribution with the theoretically predicted ones. A single histopathological slice suffices to characterize the reaction-diffusion equation dynamics through its power spectral density giving us an interpretative key in terms of infiltration and diffusion of cancer on a per-patient basis. This novel approach tackles model-parameter-inference problems for tumor-infiltration forecasting and classification and immediately informs clinical treatments. ### Competing Interest Statement The authors have declared no competing interest.