Invadopodia Formation in Cancer Cell: The Mathematical and Computational Modelling Based on Free Boundary Problem

We present a mathematical model of an individual cell to expand the simulation invadopodia formation three-dimensional (3D) domain for more realistic complexity. Simulating replication in order it be biologically relevant is important since helps us understand cancer invasion and metastasis better as well giving some insight into investigating ways stop spread this fatal disease. Invadopodia formulated using Stefan problem approach, where free boundary characterised by condition, which membrane not known advance. Level set method proposed indicate behaviour interface motion plasma membrane. An enthalpy (phase-transition problem) used describe diffusion. In addition this, we were able improve outcome, complexity different technique data set. Singularities instabilities eliminated. The results that achieved have potential helpful novel approaches or extended other methods development accurate numerical simulation.