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Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method

Author

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  • Quiroga, A.A.I.
  • Fernández, D.
  • Torres, G.A.
  • Turner, C.V.

Abstract

In this paper we present a method for estimating an unknown parameter that appears in a two dimensional non-linear reaction–diffusion model of cancer invasion. This model considers that tumor-induced alteration of micro-environmental pH provides a mechanism for cancer invasion. A coupled system reaction–diffusion describing this model is given by three partial differential equations for the 2D non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess H+ ion concentration. Each of the model parameters has a corresponding biological interpretation, for instance, the growth rate of neoplastic tissue, the diffusion coefficient, the re-absorption rate and the destructive influence of H+ ions in the healthy tissue.

Suggested Citation

  • Quiroga, A.A.I. & Fernández, D. & Torres, G.A. & Turner, C.V., 2015. "Adjoint method for a tumor invasion PDE-constrained optimization problem in 2D using adaptive finite element method," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 358-368.
    • Handle: RePEc:eee:apmaco:v:270:y:2015:i:c:p:358-368
    DOI: 10.1016/j.amc.2015.08.038
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