An integrative multiphase model for cancer cell migration under influence of physical cues from the microenvironment

Abstract

More than forty years ago Keller and Segel presented a mathematical continuum model for cell migration where chemotaxis was a main transport mechanism together with dispersion. A decade ago Chaplain and Lolas developed a model for cancer cell migration which also accounted for transport due to interaction of cells with fibers in the extracellular matrix (ECM), the so-called haptotaxis effect. Recent cancer research emphasizes the role played by physical cues from the tumor microenvironment besides the biochemical cues. Some of them are: (i) the role of cell-cell and cell-ECM adhesion; (ii) pattern formation caused by detachment of small cell clusters from the primary tumor; (iii) elevated pressure associated with the primary tumor and interstitial fluid flow; (iv) physical resistance forces from the surrounding ECM. Hence, there is a need for mathematical frameworks that can properly integrate all these aspects in a coherent formulation. We apply a multiphase continuum-based approach and consider the cancer cells and interstitial fluid as two distinct compressible phases whereas the ECM is a non-mobile component. The principle of mass and momentum balance are employed such that proliferation, apoptosis, cell force-generating mechanisms, capillary pressure and surface tension (which represent cell-cell and cell-ECM adhesion), as well as resistance forces from the microenvironment can be accounted for. We test the model for different scenarios and compare with reported experimental observations in 2D and 3D. We find that the proposed multiphase model is general enough to adequately address the above mentioned issues (i)–(iv).