A new nonlinear elliptic multilevel FEM in clinical cancer therapy planning

Abstract.In the clinical cancer therapy regional hyperthermia certain nonlinear perfusion effects inside and outside the tumor seem to play a significant role. A stationary model of such effects leads to a nonlinear Helmholtz term within an elliptic boundary value problem. The present paper reports about the application of a recently designed adaptive multilevel FEM (code NEWTON-KASKADE) to this problem. For two 3D virtual patients, nonlinear and linear models are compared. Moreover, the numerical efficiency of the new algorithm is compared with a former application of an adaptive FEM to the corresponding non stationary model PDE.

[1]  D. Rose,et al.  Analysis of a multilevel iterative method for nonlinear finite element equations , 1982 .

[2]  H. H. Pennes.  Analysis of tissue and arterial blood temperatures in the resting human forearm. 1948. , 1948, Journal of applied physiology.

[3]  P. Deuflhard,et al.  Global Inexact Newton Multilevel FEM for Nonlinear Elliptic Problems , 1998 .

[4]  Hans-Christian Hege,et al.  Hyperthermia Treatment Planning in Clinical Cancer Therapy:Modelling, Simulation, and Visualization , 1997 .

[5]  Jens Lang,et al.  Adaptive Multilevel Solution of Nonlinear Parabolic PDE Systems - Theory, Algorithm, and Applications , 2001, Lecture Notes in Computational Science and Engineering.

[6]  W. Hackbusch,et al.  Analysis of a damped nonlinear multilevel method , 1989 .

[7]  Peter Bastian,et al.  Adaptive Multigrid Methods: The UG Concept , 1994 .

[8]  Randolph E. Bank,et al.  PLTMG - a software package for solving elliptic partial differential equations: users' guide 8.0 , 1998, Software, environments, tools.

[9]  M. Seebass,et al.  Impact of nonlinear heat transfer on temperature control in regional hyperthermia , 1999, IEEE Transactions on Biomedical Engineering.

[10]  J. Rhee,et al.  Implication of Blood Flow in Hyperthermic Treatment of Tumors , 1984, IEEE Transactions on Biomedical Engineering.

[11]  Peter Deuflhard,et al.  Adaptive Multilevel FEM as Decisive Tools in the Clinical Cancer Therapy Hyperthermia , 1998 .

[12]  R. Roitzsch,et al.  KASKADE 3.0 - An Object Oriented Adaptive Finite Element Code , 1995 .

[13]  H. Rentz-Reichert,et al.  UG – A flexible software toolbox for solving partial differential equations , 1997 .