Cancer progression is associated with alternations in the cytoskeletal architecture of cells and, consequently, their mechanical properties such as stiffness. Changing the mechanics of cells enables cancer cells to migrate and invade to distant organ sites. This process, metastasis, is the main reason for cancer-related mortality. Cell migration is an essential step toward increasing the invasive potential of cells. Although many studies have shown that the migratory speed and the invasion of cells can be inversely correlated to the stiffness of cells, some other investigations indicate exactly opposing results. In the current work, based on the strain energy stored in cells due to the contractile forces, we defined an energy-dependent term, migratory index, to approximate how changes in the mechanical properties of cells influence cell migration required for cancer progression. Cell migration involves both cell deformation and force transmission within cells. The effects of these two parameters can be represented equally by the migratory index. Our mechanical modeling and computational study show that cells depending on their shape, size, and other physical parameters, have a maximum migratory index taking place at a specific range of cell bulk stiffness, indicating the most favorable conditions for invasive mobility. This approximate model can be used to explain why the stiffness of cells varies during cancer progression.  We believe that the stiffness of invasive cells depending on the stiffness of their non-invasive counterparts is either decreased or increased to reach the critical condition in which the mobility potential of cells is approximated to be maximum.

Data were extracted from COMSOL Multiphysics (Solid mechanics Module/Hyperelastic materials)   

You can find extracted data from "Parameters_on_Migratory_Index". To repeat the simulation, refer to "simulation_setting" to see the set parameters to run the simulation. The 2D model can be found from "Cell_CAD_Model".