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Computational insights into tumor invasion dynamics: A finite element approach

Author

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  • Irum, Saba
  • Almakayeel, Naif
  • Deebani, Wejdan

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.

Suggested Citation

  • Irum, Saba & Almakayeel, Naif & Deebani, Wejdan, 2025. "Computational insights into tumor invasion dynamics: A finite element approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 814-829.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:814-829
    DOI: 10.1016/j.matcom.2024.10.026
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