  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.
