Suitability of eigenvalue beam-forming for discrete multi-frequency hyperthermia treatment planning

Purpose Thermal dose delivery in microwave hyperthermia for cancer treatment is expected to benefit from the introduction of ultra-wideband (UWB)-phased array applicators. A full exploitation of the combination of different frequencies to improve the deposition pattern is, however, a nontrivial problem. It is unclear whether the cost functions used for hyperthermia treatment planning (HTP) optimization in the single-frequency setting can be meaningfully extended to the UWB case. Method We discuss the ability of the eigenvalue (EV) and a novel implementation of iterative-EV (i-EV) beam-forming methods to fully exploit the available frequency spectrum when a discrete set of simultaneous operating frequencies is available for treatment. We show that the quadratic power deposition ratio solved by the methods can be maximized by only one frequency in the set, therefore rendering EV inadequate for UWB treatment planning. We further investigate whether this represents a limitation in two realistic test cases, comparing the thermal distributions resulting from EV and i-EV to those obtained by optimizing for other nonlinear cost functions that allow for multi-frequency. Results The classical EV-based single-frequency HTP yields systematically lower target SAR deposition and temperature values than nonlinear HTP. In a larynx target, the proposed single-frequency i-EV scheme is able to compensate for this and reach temperatures comparable to those given by global nonlinear optimization. In a meninges target, the multi-frequency setting outperforms the single-frequency one, achieving better target coverage and 0.5 circle C higher T90 in the tumor than single-frequency-based HTP. Conclusions Classical EV performs poorly in terms of resulting target temperatures. The proposed single-frequency i-EV scheme can be a viable option depending on the patient and tumor to be treated, as long as the proper operating frequency can be selected across a UWB range. Multi-frequency HTP can bring a considerable benefit in regions typically difficult to treat such as the brain.