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.

This paper introduces and discusses an innovative approach to focus the electromagnetic power carried by a vector field into a target point, while keeping the field level bounded elsewhere. To overcome the complexity of the underlying NP-hard problem, we introduce a multi-objective optimization framework based on convex programming subproblems. Notably, such a strategy has the unique capability of achieving the globally optimal solution by means of local search algorithms. A numerical analysis is reported to assess the methods' performance, including a comparison with previous contributions. The proposed approach is herein presented in the case of 2D vector fields (transverse electric polarization) but it can be easily extended to the general 3D case.

Abstract-The problem of field focusing onto a target location in an unknown scenario is considered. In particular, we devise an adaptive procedure in which first an image of the unknown region where the target point is located is formed via the linear sampling method (LSM). Then, the LSM result is used also to define the excitations coefficients for the array elements needed to focus the field. This novel approach to focusing is described and tested with numerical examples.

Two strategies to focus time harmonic scalar fields in known inhomogeneous lossy media are compared. The first one is the Inverse Filter (IF) method, which faces the focusing task as the synthesis of a nominal field. The second one is the Constrained Power Focusing Optimization (CPFO) method, which tackles the problem in terms of constrained mask constrained power optimization. Numerical examples representative of focusing in noninvasive microwave hyperthermia are provided to show that CPFO is able to outperform IF, thanks to the additional degrees of freedom arising from the adopted power synthesis formulation.