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Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia

Please always quote using this URN: urn:nbn:de:0297-zib-3739
  • The paper surveys recent progress in a joint mathematical-medical project on cancer therapy planning. Within so-called regional hyperthermia the computational task is to tune a set of coupled radiofrequency antennas such that a carefully measured tumor is locally heated, but any outside hot spots are avoided. A mathematical model of the whole clinical system -- air, applicator with antennas, water bolus, individual patient body -- involves Maxwell's equations in inhomogeneous media and a parabolic bioheat transfer equation, which represents a simplified model of heat transfer in the human body (ignoring strong blood vessel heat transport). Both PDEs need to be computed fast and to medical reliability (!) on a workstation within a clinical environment. This requirement triggered a series of new algorithmic developments to be reported here, among which is an adaptive multilevel FEM for Maxwell's equations, which dominates the numerical simulation time. In total, however, the main bulk of computation time (see Table 3 in Section 4 below) still goes into segmentation -- a necessary preprocessing step in the construction a 3D virtual patient from the input of a stack of 2D computed tomograms (left out here).

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Author:Peter Deuflhard, Martin Seebass
Document Type:ZIB-Report
Tag:Maxwell's equations; finite elements; hyperthermia; nonlinear heat transfer
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Cxx Physiological, cellular and medical topics / 92C50 Medical applications (general)
Date of first Publication:1998/11/11
Series (Serial Number):ZIB-Report (SC-98-30)
Published in:Appeared in: Choi-Hong Lai, Peter E. Björstad, Mark Cross und Olof O. Widlund (eds.), Proc. Eleventh International Conference on: Domain Decomposition Methods in Sciences and Engineering, DDM-org Press, Bergen, pp. 403-414 (1999)