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An image-driven parameter estimation problem for a reaction–diffusion glioma growth model with mass effects

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Abstract

We present a framework for modeling gliomas growth and their mechanical impact on the surrounding brain tissue (the so-called, mass-effect). We employ an Eulerian continuum approach that results in a strongly coupled system of nonlinear Partial Differential Equations (PDEs): a reaction-diffusion model for the tumor growth and a piecewise linearly elastic material for the background tissue. To estimate unknown model parameters and enable patient-specific simulations we formulate and solve a PDE-constrained optimization problem. Our two main goals are the following: (1) to improve the deformable registration from images of brain tumor patients to a common stereotactic space, thereby assisting in the construction of statistical anatomical atlases; and (2) to develop predictive capabilities for glioma growth, after the model parameters are estimated for a given patient. To our knowledge, this is the first attempt in the literature to introduce an adjoint-based, PDE-constrained optimization formulation in the context of image-driven modeling spatio-temporal tumor evolution. In this paper, we present the formulation, and the solution method and we conduct 1D numerical experiments for preliminary evaluation of the overall formulation/methodology.

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Correspondence to George Biros.

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Hogea, C., Davatzikos, C. & Biros, G. An image-driven parameter estimation problem for a reaction–diffusion glioma growth model with mass effects. J. Math. Biol. 56, 793–825 (2008). https://doi.org/10.1007/s00285-007-0139-x

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  • DOI: https://doi.org/10.1007/s00285-007-0139-x

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