Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on both biochemical signaling and the mechanical properties of cancer cells, adipocytes, and other key components of adipose tissue. We model breast cancer invasion into adipose tissue using discrete element method simulations of active, cohesive spherical particles (cancer cells) invading into confluent packings of deformable polyhedra (adipocytes). We quantify the degree of invasion by calculating the interfacial area At between cancer cells and adipocytes. We determine the long-time value of At vs the activity and strength of the cohesion between cancer cells, as well as the mechanical properties of the adipocytes and extracellular matrix in which adipocytes are embedded. We show that the degree of invasion collapses onto a master curve as a function of the dimensionless energy scale Ec, which grows linearly with the cancer cell velocity persistence time and fluctuations, is inversely proportional to the system pressure, and is offset by the cancer cell cohesive energy. When E (c )> 1, cancer cells will invade the adipose tissue, whereas for E- c < 1, cancer cells and adipocytes remain de-mixed. We also show that At decreases when the adipocytes are constrained by the ECM by an amount that depends on the spatial heterogeneity of the adipose tissue.
