Three-dimensional Simulation of Invadopodia Formation Associated with Ligand and Signal Stimulation

Muhammad Akmal, Ramlee (2024) Three-dimensional Simulation of Invadopodia Formation Associated with Ligand and Signal Stimulation. Masters thesis, Universiti Malaysia Sarawak.

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Abstract

The simulation of invadopodia replication holds significance in establishing its biological relevance, as it contributes to a deeper comprehension of cancer invasion and metastasis. Additionally, it offers valuable insights into potential strategies for impeding the dissemination of this life-threatening disease. In this study, we present a mathematical model that describes the behaviour of an individual cell, with the aim of extending the simulation of invadopodia creation to a three-dimensional (3D) environment, thereby incorporating a higher level of realism and complexity. The formation of invadopodia is approached utilising the Stefan problem framework, wherein the cell membrane is defined by the Stefan free boundary condition, which entails that the boundary membrane is not predetermined. The proposed method for characterising the behaviour of the cell interface and the mobility of the plasma membrane is the level set method. The modelling process incorporated the following parameters: ECM c, MMPs f, ligands c*, and signal σ. Furthermore, we enhanced the fidelity of the simulation results by employing an alternative simulation methodology and domain, along with a distinct dataset. This was achieved by applying the finite element method (FEM) and employing software tools such as FreeFem++ for simulation and Gmsh for mesh generation. The presence of singularities and instabilities was successfully eradicated and our comparison of the findings demonstrates their near resemblance to the actual ones. The attained outcomes have the potential to offer valuable insights for innovative methodologies and can be further applied to enhance the precision of numerical simulations.

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