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A high intensity focused ultrasound (HIFU) treatment has a very complex therapy planning structure. In this thesis we introduce a workflow on the basis of a decomposition of the therapy plan into controllable but coupled subproblems. Under certain assumptions, including the decoupling of these subproblems, we first concentrate on the maximisation of the sonication area on a patient surface. The sound waves form a double cone in the center of which the main energy transfer to the tumour tissue takes place. A maximally opened cone allows for the use of as many degrees of freedom as possible which represents a good basis for further computations. The cone is restricted by so called areas of risk, which are healthy tissue domains. These areas should not be affected by the ultrasound. For a future simulation it is necessary to know about the temperature distribution in the focal points depending on the available parameters. We establish a short-cut model to overcome the time-consuming problem of solving the nonlinear wave equation at each data point. This short-cut model characterises the diffusion of heat using the heat equation. We solve the heat equation by using Green´s functions.

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Xenia-Rosemarie Reit, born in 1986 in Idar-Oberstein, Germany, studied mathematics and physics at the TU Kaiserslautern. Since 2011 she is working as a research assistant at the Goethe University Frankfurt in the institute for didactics of mathematics and informatics.

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