“…The temporal rate of change in viable and dead tumor tissue at any location within the tumor equals the amount of mass that is pushed, transported, and pulled due to cell motion, adhesion, and tissue pressure, plus the net result of production and destruction of mass due to cell proliferation and death:
The rate of change in the volume fraction ρ i of cell species i ( V : viable tumor; D : dead tumor; H : host) is specified throughout the computational domain by balancing net creation ( S i : proliferation minus apoptosis and necrosis; see below) with cell advection (∇·( u
i ρ i ), where u
i is the velocity of the cell species) and cell-cell and cell-ECM interactions (adhesion, cell incompressibility, chemotaxis, and haptotaxis, incorporated in a flux J
i ) [31], [32]. The reticular network within the lymph node contains a variety of extracellular matrix proteins, many of which are known ligands for integrin cell surface adhesion receptors [42], [43]. Cell-cell and cell-ECM mechanical interactions are modeled through J using a generalized Fick's Law [31].…”