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Journal of Mathematical Biology

, Volume 56, Issue 6, pp 793–825 | Cite as

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

  • Cosmina Hogea
  • Christos Davatzikos
  • George Biros
Article

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.

Mathematical Subject Classification (2000)

92C10 92C55 92C50 92B05 92C15 65K99 74S10 74S20 74G15 74G75 74L15 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Cosmina Hogea
    • 1
  • Christos Davatzikos
    • 1
  • George Biros
    • 2
  1. 1.Section of Biomedical Image Analysis, Department of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Departments of Mechanical Engineering and Applied Mechanics, and Computer and Information ScienceUniversity of PennsylvaniaPhiladelphiaUSA

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