Mathematical Cancer Therapy Planning in Deep Regional Hyperthermia

Please always quote using this URN: urn:nbn:de:0297-zib-14204
  • This paper surveys the required mathematics for a typical challenging problem from computational medicine, the cancer therapy planning in deep regional hyperthermia. In the course of many years of close cooperation with clinics, the medical problem gave rise to quite a number of subtle mathematical problems, part of which had been unsolved when the common project started. Efficiency of numerical algorithms, i.e. computational speed and monitored reliability, play a decisive role for the medical treatment. Off-the-shelf software had turned out to be not sufficient to meet the requirements of medicine. Rather, 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, a virtual lab, including 3D 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 analyzed and realized over the individual patient's geometry. Our new techniques had an impact on the specificity of the individual patients' treatment and on the construction of an improved hyperthermia applicator.

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Author:Peter Deuflhard, Anton Schiela, Martin WeiserORCiD
Document Type:ZIB-Report
Tag:Maxwell equations; hyperthermia therapy planning; mathematical modelling; parameter identification; state constraints
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Mxx Numerical methods [See also 90Cxx, 65Kxx]
65-XX NUMERICAL ANALYSIS
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics
Date of first Publication:2011/10/21
Series (Serial Number):ZIB-Report (11-39)
ISSN:1438-0064
Published in:Appeared in: Acta Numerica 21: 307-378, 2012