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Source Localization of Reaction-Diffusion Models for Brain Tumors

  • Rym JaroudiEmail author
  • George Baravdish
  • Freddie Åström
  • B. Tomas Johansson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9796)

Abstract

We propose a mathematically well-founded approach for locating the source (initial state) of density functions evolved within a nonlinear reaction-diffusion model. The reconstruction of the initial source is an ill-posed inverse problem since the solution is highly unstable with respect to measurement noise. To address this instability problem, we introduce a regularization procedure based on the nonlinear Landweber method for the stable determination of the source location. This amounts to solving a sequence of well-posed forward reaction-diffusion problems. The developed framework is general, and as a special instance we consider the problem of source localization of brain tumors. We show numerically that the source of the initial densities of tumor cells are reconstructed well on both imaging data consisting of simple and complex geometric structures.

Keywords

Source Term Forward Problem Gray Matter Region Ordinary Differential Equation Model Tumor Cell Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Rym Jaroudi
    • 1
    Email author
  • George Baravdish
    • 1
  • Freddie Åström
    • 2
  • B. Tomas Johansson
    • 1
    • 3
  1. 1.Linköping UniversityLinköpingSweden
  2. 2.Heidelberg Collaboratory for Image ProcessingHeidelberg UniversityHeidelbergGermany
  3. 3.Aston UniversityBirminghamUK

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