Focusing time harmonic scalar fields in non-homogenous lossy media: Inverse filter vs. constrained power focusing optimization

Abstract

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.

Thermal and Microwave Constrained Focusing for Patient-Specific Breast Cancer Hyperthermia: A Robustness Assessment

“…First, the relationship between electromagnetic and thermal focusing has been clarified. Then, a performance analysis has been carried out for the OCPF [8], [12], [13], a recently proposed strategy that is able to focus the electromagnetic field and preserve healthy tissues. In particular, efforts have been devoted to understand the conditions that ensure the effectiveness of OCPF-based planning tools and treatment.…”

“…Notably, methods based on the time reversal principle [10] (which actually does not hold true in lossy media) also cannot foresee the presence of hot spots. A more detailed discussion of time reversal and its developments [11] in comparison to OCPF can be found in [12] and [13], respectively.…”

“…Obviously, such an assessment is crucial to guarantee that any focusing method allows effective and safe treatments, and is also of particular interest because of the aforementioned improved performances of OCPF [12], [13]. To this end, we have built a numerical testbed of 2-D anthropomorphic phantoms, derived from realistic images of four different breast typologies [17], [18], to simulate the treatment of early-stage tumors.…”

Constrained power focusing of vector fields: an innovative globally optimal strategy

“…to achieve the globally optimal solution and to control power deposition in the whole region of interest), one should tackle the problem by formulating a suitable optimization strategy. However, while for scalar fields the resulting constrained optimization problem can be efficiently and effectively addressed via convex programming (CP), [10][11][12][13][14] this is not anymore the case for vector fields. As a matter of fact, in such a case, the underlying optimization problem can be shown to be a non-deterministic polynomial-time hard (NP-hard) problem.…”

Constrained Power Focusing in Inhomogeneous Media as a Polarization Optimization

“…Inverse Filter [6,11] takes partially into account this aspect of the focusing problem as it relies on the enforcement of a specific field pattern, which ideally should be a Dirac function of the space coordinates centered at the target point. In this respect, the selection of the reference pattern is crucial and affects the focusing performances so that obtained focused field (which is unavoidably different from the target one) will be reference pattern dependent.…”