Source localization of reaction-diffusion models for brain tumors

Rym Jaroudi*, George Baravdish, Freddie Åström, B. Tomas Johansson

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationPattern recognition
Subtitle of host publication38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings
EditorsBodo Rosenhahn, Bjoern Andres
Place of PublicationCham (CH)
PublisherSpringer
Pages414-425
Number of pages12
ISBN (Electronic)978-3-319-45886-1
ISBN (Print)978-3-319-45885-4
DOIs
Publication statusPublished - 27 Aug 2016
Event38th German Conference on Pattern Recognition - Hannover, Germany
Duration: 12 Sep 201615 Sep 2016

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume9796
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference38th German Conference on Pattern Recognition
Abbreviated titleGCPR 2016
CountryGermany
CityHannover
Period12/09/1615/09/16

Fingerprint

Brain Tumor
Source Localization
Reaction-diffusion Model
Tumors
Brain
Inverse problems
Probability density function
Cells
Imaging techniques
Forward Problem
Reaction-diffusion Problems
Geometric Structure
Ill-posed Problem
Complex Structure
Density Function
Nonlinear Model
Tumor
Regularization
Inverse Problem
Unstable

Cite this

Jaroudi, R., Baravdish, G., Åström, F., & Johansson, B. T. (2016). Source localization of reaction-diffusion models for brain tumors. In B. Rosenhahn, & B. Andres (Eds.), Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings (pp. 414-425). (Lecture Notes in Computer Science; Vol. 9796). Cham (CH): Springer. https://doi.org/10.1007/978-3-319-45886-1_34
Jaroudi, Rym ; Baravdish, George ; Åström, Freddie ; Johansson, B. Tomas. / Source localization of reaction-diffusion models for brain tumors. Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings. editor / Bodo Rosenhahn ; Bjoern Andres. Cham (CH) : Springer, 2016. pp. 414-425 (Lecture Notes in Computer Science).
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Jaroudi, R, Baravdish, G, Åström, F & Johansson, BT 2016, Source localization of reaction-diffusion models for brain tumors. in B Rosenhahn & B Andres (eds), Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings. Lecture Notes in Computer Science, vol. 9796, Springer, Cham (CH), pp. 414-425, 38th German Conference on Pattern Recognition, Hannover, Germany, 12/09/16. https://doi.org/10.1007/978-3-319-45886-1_34

Source localization of reaction-diffusion models for brain tumors. / Jaroudi, Rym; Baravdish, George; Åström, Freddie; Johansson, B. Tomas.

Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings. ed. / Bodo Rosenhahn; Bjoern Andres. Cham (CH) : Springer, 2016. p. 414-425 (Lecture Notes in Computer Science; Vol. 9796).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - 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.

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Jaroudi R, Baravdish G, Åström F, Johansson BT. Source localization of reaction-diffusion models for brain tumors. In Rosenhahn B, Andres B, editors, Pattern recognition: 38th German Conference, GCPR 2016, Hannover, Germany, September 12-15, 2016, Proceedings. Cham (CH): Springer. 2016. p. 414-425. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-45886-1_34