In this paper, we address the problem of microwave hyperthermia. In particular, we first introduce simple tools to understand the relationship between thermal and electromagnetic power focusing. Then, we assess the electromagnetic and thermal performances of a recently proposed strategy to design array applicators. Contrary to common approaches, such a strategy allows a punctual control of power deposition, which is crucial for effective treatment planning. With respect to breast cancer hyperthermia, we analyze the robustness of the strategy against inaccuracies based on the knowledge of the scenario, in a quantitative manner. This analysis allows us to draw useful guidelines on the accuracy of patient-specific information required to guarantee the effectiveness of treatment.

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We introduce a novel strategy to synthesize an antenna array capable to focus a field in an unknown scenario. The underlying power synthesis problem is efficiently solved via convex programming and using an approximation of the fields radiated by the array elements. This approximation stems from an original exploitation of the equation underlying the Linear Sampling Method. As such, the proposed strategy takes advantage of the broad applicability of this well-known imaging approach. Some numerical examples are given to illustrate the performance of the strategy.