NUMERICAL SIMULATION OF UNSTEADY SIGNAL TRANSDUCTION DURING THE FORMATION OF INVADOPODIA USING LEVEL SET METHOD

The finger-like protrusions formed by an invasive cancer cell known as invadopodia is actively observed recently because of this formation on the cancer invasion. The signal on the interface which is stimulated upon contact between epidermal growth factor receptor and ligand, is investigated to be the start of invadopodia formation. In this research, a model of invadopodia formation with signal variable is formulated in two dimensions. The plasma membrane is assumed to be free boundary. The signal is in an unsteady state. The equation of signal is represented by heat-like equation with time-dependent boundary condition. Trigonometry types of the boundary condition which are sine and cosine function are tested to identify the most suitable boundary condition represented the free boundary. The plasma membrane is considered as zero level set function. The membrane moves by the velocity of the signal inside the cell. To handle the free boundary problem, the level set method combining features of ghost method, interpolation and extrapolation method is applied to solve the model numerically. Our result shows that the free boundary is moved at different positions and seen to move inward meaning that the boundary has shrunk. Cosine function is discovered to fit the boundary conditions since the boundary solutions are stable across the time. The computation of the signal density profiles displayed highest density on the membrane.