Level set method for free boundary of invasive cancer cell using different functions of matrix metalloproteinases

Abstract

The secondary tumor is stated to be more dangerous among cancer patients and this tumor is created through metastasis. Metastasis is the process of spreading a tumor from the primary location to the second part of the human body. This is an unpleasant problem among cancer patients because metastasis can contribute to high mortality cases among them. The presence of finger-like protrusions on the plasma membrane of cancer cells is known as the invadopodia. This structure can contribute to cancer cell invasion through the metastasis process. The formation of invadopodia involves several molecular interactions between extracellular matrix (ECM), ligand, actin, and matrix metalloproteinases (MMPs). The degradation of the ECM by the MMPs is mentioned as the starting point for the occurrence of cancer cell invasion. In this paper, the concentration of MMPs is taken in several functions of g to observe the formation of invadopodia on the plasma membrane. Two-dimensional mathematical model of ligand and signal is solved numerically using the method of level set, ghost fluid with linear extrapolation, and finite-difference. Credit is given to the level set method which successfully detected the movement of the free boundary interface (plasma membrane) by setting the interface as a zero-level set function. Also, the neighboring meshes can be identified using this method. Results showed that the above-mentioned integrated methods effectively describe the movement of the free boundary interface and this directly points out the formation of protrusions on the plasma membrane.