Computational modeling of the physical features that influence breast cancer invasion into adipose tissue

Breast cancer invasion into adipose tissue strongly influences disease progression and metastasis. The degree of cancer cell invasion into adipose tissue depends on numerous biochemical and physical properties of cancer cells, adipocytes, and other key components of adipose tissue. We model breast cancer invasion into adipose tissue as a physical process by carrying out 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 $A_t$ between cancer cells and adipocytes. We determine the long-time value of $A_t$ versus the activity and strength of the cohesion between cancer cells, as well as mechanical properties of the adipocytes and extracellular matrix (ECM) in which the adipocytes are embedded. We show that the degree of invasion collapses onto a master curve by plotting it versus a dimensionless energy scale $E_c$, which grows linearly with mean-square fluctuations and persistence time of the cancer cell velocities, is inversely proportional to the pressure of the system, and has an offset that increases with the cancer cell cohesive energy. The condition, $E_c\gg 1$, indicates that cancer cells will invade the adipose tissue, whereas for $E_c\ll 1$, the cancer cells and adipocytes remain demixed. We also show that constraints on adipocyte positions by the ECM decrease $A_t$ relative to that obtained for unconstrained adipocytes. Finally, spatial heterogeneity in structural and mechanical properties of the adipocytes in the presence of ECM impedes invasion relative to adipose tissue with uniform properties.