We describe an optimization process specially designed for regional hyperthermia of deep-seated tumors in order to achieve desired steady-state temperature distributions. A nonlinear three-dimensional heat transfer model based on temperature-dependent blood perfusion is applied to predict the temperature. Using linearly implicit methods in time and adaptive multilevel finite elements in space, we are able to integrate efficiently the instationary nonlinear heat equation with high accuracy. Optimal heating is obtained by minimizing an integral objective function which measures the distance between desired and model predicted temperatures. A sequence of minima is calculated from successively improved constant-rate perfusion models employing a damped Newton method in an inner iteration. We compare temperature distributions for two individual patients calculated on coarse and fine spatial grids and present numerical results of optimizations for a Sigma 60 Applicator of the BSD 2000 Hyperthermia System.
This paper investigates the effects of the three-dimensional arrangement of antennae and frequency on temperature distributions that can be achieved in regional hyperthermia using an electromagnetic phased array. It compares the results of power-based and temperature-based optimization. Thus, one is able to explain the discrepancies between previous studies favouring more antenna rings on the one hand and more antennae per ring on the other hand. The sensitivity of the results is analysed with respect to changes in amplitudes and phases, as well as patient position. This analysis can be used for different purposes. First, it provides additional criteria for selecting the optimal frequency. Secondly, it can be used for specifying the required phase and amplitude accuracy for a real phased array system. Furthermore, it may serve as a basis for technological developments in order to reduce both types of sensitivities described above.
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