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Galerkin finite element method for cancer invasion mathematical model

Ganesan, Sashikumaar and Lingeshwaran, Shangerganesh (2017) Galerkin finite element method for cancer invasion mathematical model. In: Computers & Mathematics with Applications, 73 (12). pp. 2603-2617. ISSN 08981221

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Official URL: https://doi.org/10.1016/j.camwa.2017.04.006


A finite element scheme for the solution of a cancer invasion model is proposed. The cancer dynamics model consists of three coupled partial differential equations which describe the evolution of cancer cell density, extra cellular matrix and the matrix degrading enzymes. The model incorporates proliferation and haptotaxis effect of cancer cells, their interaction with extracellular matrix, the production of matrix degrading enzymes and consequent degradation of the extracellular matrix. The coupled partial differential equations are discretized in space with the standard Galerkin finite elements and in time with the Crank–Nicolson method. Moreover, the nonlinear terms in the coupled equations are treated semi-implicitly in the finite element scheme. The numerical scheme is validated with numerical results taken from the literature. In addition to the mesh convergence study, the effects of haptotactic rate, proliferation rate and remodelling rate of matrix components of the considered mathematical model are investigated.

Item Type: Journal Article
Publication: Computers & Mathematics with Applications
Publisher: Elsevier Ltd
Additional Information: The copyright for this article belongs to the Authors
Keywords: Cancer invasion; Finite element simulations; Haptotaxis effect; PDE cancer model
Department/Centre: Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited: 30 May 2022 04:37
Last Modified: 30 May 2022 04:37
URI: https://eprints.iisc.ac.in/id/eprint/72819

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