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Numerical solution of metastatic tumor growth models with treatment

Author

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  • Bulai, I.M.
  • De Bonis, M.C.
  • Laurita, C.

Abstract

In this paper we introduce an efficient numerical method in order to solve Volterra integral equations (VIE) of the second type. We are motivated by the fact that the coupled PDE-ODE model, used to describe the metastatic tumor growth, can be reformulated in terms of VIE, whose unknowns are biological observables, such as the cumulative number of metastases and the total metastatic mass. Here in particular we focused our attention on the 2D non autonomous case, where also the treatment is considered. After reformulating the model as a VIE and introducing and studying the numerical method, we first compare it with a method previously introduced by the authors for the 1D case, and extended to the 2D case only for the sake of comparison, in term of efficiency in the run time execution. Secondly, we present numerical results on the effectiveness of different treatment protocols on the total cumulative number of metastases and the total metastatic mass.

Suggested Citation

  • Bulai, I.M. & De Bonis, M.C. & Laurita, C., 2025. "Numerical solution of metastatic tumor growth models with treatment," Applied Mathematics and Computation, Elsevier, vol. 484(C).
    • Handle: RePEc:eee:apmaco:v:484:y:2025:i:c:s0096300324004491
    DOI: 10.1016/j.amc.2024.128988
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    References listed on IDEAS

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    1. Bulai, I.M. & De Bonis, M.C. & Laurita, C. & Sagaria, V., 2023. "Modeling metastatic tumor evolution, numerical resolution and growth prediction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 721-740.
    2. Maxim V. Polyakov & Valeria V. Ten, 2024. "Simulation tumor growth in heterogeneous medium based on diffusion equation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 35(01), pages 1-16, January.
    3. Sébastien Benzekry & Clare Lamont & Afshin Beheshti & Amanda Tracz & John M L Ebos & Lynn Hlatky & Philip Hahnfeldt, 2014. "Classical Mathematical Models for Description and Prediction of Experimental Tumor Growth," PLOS Computational Biology, Public Library of Science, vol. 10(8), pages 1-19, August.
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