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

Muhammad Akmal Ramlee (), Nuha Loling Othman () and Takashi Suzuki
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Muhammad Akmal Ramlee: Faculty of Computer Science and Information Technology, Universiti Malaysia Sarawak, Jalan Datuk Mohd Musa, 94300 Kota Samarahan, Sarawak, Malaysia
Nuha Loling Othman: Faculty of Computer Science and Information Technology, Universiti Malaysia Sarawak, Jalan Datuk Mohd Musa, 94300 Kota Samarahan, Sarawak, Malaysia
Takashi Suzuki: Center for Mathematical Modeling and Data Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka City 560-8531, Osaka, Japan

Mathematics, 2023, vol. 11, issue 14, 1-17

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

Keywords: invadopodia; individual cell model; free boundary problem; finite element method; Stefan problem; level set method; phase transition; enthalpy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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