Titlebar

Export bibliographic data
Literature by the same author
plus on the publication server
plus at Google Scholar

 

Mathematical cancer therapy planning in deep regional hyperthermia

Title data

Deuflhard, Peter ; Schiela, Anton ; Weiser, Martin:
Mathematical cancer therapy planning in deep regional hyperthermia.
In: Acta Numerica. Vol. 21 (2012) . - pp. 307-378.
ISSN 0962-4929
DOI: https://doi.org/10.1017/S0962492912000049

Review:

Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

This paper surveys the mathematics required for a typically challenging problem from computational medicine: cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem has given rise to many subtle mathematical problems, some of which were unsolved when the project started. Efficiency of numerical algorithms, i.e., computational speed and monitored reliability, plays a decisive role in the medical treatment. Off-the-shelf software had turned out to be insufficient to meet the requirements of medicine. Instead, new mathematical theory as well as new numerical algorithms had to be developed. In order to make our algorithms useful in the clinical environment, new visualization software, i.e., a ‘virtual lab’, including three-dimensional geometry processing of individual virtual patients, had to be designed and implemented. Moreover, before the problems could be attacked by numerical algorithms, careful mathematical modelling had to be done. Finally, parameter identification and constrained optimization for the PDEs had to be newly analysed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the treatment of individual patients and on the construction of an improved hyperthermia applicator.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version is published at the Konrad- Zuse-Zentrum für Informationstechnik, Berlin as ZIB-Report 11-39
Keywords: Maxwell equations; hyperthermia therapy planning; mathematical modelling; parameter identification; state constraints
Subject classification: Mathematics Subject Classification Code: 65-02 (92C50)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Profile Fields
Profile Fields > Advanced Fields
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 19 Mar 2015 08:00
Last Modified: 23 Mar 2015 12:20
URI: https://eref.uni-bayreuth.de/id/eprint/8214