A multiphase model for exploring tumor cell migration driven by autologous chemotaxis

It has been demonstrated that interstitial fluid (IF) flow can play a crucial role in tumor cell progression. In the seminal works by Swartz and collaborators (Fleury et al., 2006; Shields et al., 2007) it was discovered that due to this flow, chemokine ligands secreted by tumor cells selectively tend to bind to receptors (CCR7) on the downstream side of the cells that in turn stimulate cells to migrate in the direction of the flow. This migration process was denoted as autologous chemotaxis. Previous mathematical modeling of autologous chemotaxis apparently has been restricted to single-phase considerations. The purpose of this work is to explore how a multiphase approach can be used where the fluid and cancer cells are treated as two separate phases with their own momentum balance equations. A mathematical model is derived that sheds light on essential nonlinear coupling mechanisms and interactions that are involved. The role played by fluid-ECM (friction type of term) and cell-ECM interaction forces (adhesion forces) are demonstrated. In particular, a fluid generated stress term in the mathematical expression for the cell velocity is highlighted. This term reflects how the flowing fluid will try to push the cancer cells in the downstream direction whose effect must be counterbalanced by the cancer cells by creating a sufficiently strong cell-ECM resistance force. Moreover, in order to represent the autologous chemotaxis migration mechanism we include (i) a component to represent stagnant ECM concentration (collagen); (ii) a chemical component representing chemokine that can convect with the fluid; and (iii) a third chemical component to represent protease secreted by the cancer cells which is able to release ECM-bound chemokine through proteolytic activity. The resulting model allows us to demonstrate how the autologous chemotaxis transport mechanism is governed by formation of chemokine concentration gradients that are asymmetric and skewed in the flow direction. We test the model behavior for a flow system with an external imposed pressure gradient which is comparable with the laboratory experiments by Swartz and collaborators. Sensitivity to changes in circumstances like blocking of the CCR7 receptor needed for autologous chemotaxis and elimination of the pressure driven IF flow (i.e., no flow) are explored and discussed. We also illustrate the model behavior in an envisioned tumor setting where increased IF flow is produced from leaky blood vessels that sit on the inside of the tumor. An increased fluid flow towards the region on the outside of the tumor is then generated where it is adsorbed by lymphatic vessels and gives rise to a characteristic elevated IF pressure profile that decreases at the tumor periphery. In turn, this results in an autologous chemotactic driven migration of cancer cells at the rim of the tumor. The simulation illustrates how the autologous chemotactic cell migration mechanism discovered by Swartz and collaborators possibly can be used as a means for metastasis by generating aggressive cell migration towards lymphatic vessels.