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

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

Applied Mathematics and Computation, 2015, vol. 270, issue C, 358-368

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.

Keywords: Reaction–diffusion 2D equation; Tumor invasion; PDE-constrained optimization; Adjoint method; Adaptive finite element method; Splitting method (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:270:y:2015:i:c:p:358-368

DOI: 10.1016/j.amc.2015.08.038

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