Computational insights into tumor invasion dynamics: A finite element approach

Saba Irum, Naif Almakayeel and Wejdan Deebani

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 229, issue C, 814-829

Abstract: The finite element scheme is proposed and analyzed for the solution of an acid-mediated tumor invasion model. The reaction–diffusion equation shows the evolution in the tumor cell density, H+ ions concentration, and healthy tissue density over time. The coupled non-linear partial differential equations are discretized in time with the implicit Euler method and in space with standard Galerkin finite element. To solve the non-linear and coupled terms of the system a fixed point iteration scheme is presented. Moreover, a mass-lumped scheme is adopted to reduce the computation cost. The cut-off method is used to compute the bounded solutions of the PDEs. Finally, The effects of proliferation rate and healthy tissue degradation rate are investigated.

Keywords: Tumor invasion; Finite element; Acid mediated model; Spatial–temporal discretization; Fixed Point algorithm; Mathematical modeling of tumor (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:229:y:2025:i:c:p:814-829

DOI: 10.1016/j.matcom.2024.10.026

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