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

Abstract

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∘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.

Iterative time-reversal for multi-frequency hyperthermia

“…Moreover, these modifications only apply to the single-frequency scenario. In a multifrequency setting, the fundamental single-frequency limitation of the EV cost function (SAR SAR T R ) needs to be resolved to fully exploit the treatment capabilities of wide-band applicators (Zanoli and Trefná 2020). Recently, an emerging time-and frequency-multiplexed beam-forming method has been proposed by Kuehne et al (2020).…”

“…where SAR T is the average SAR in the target, and SAR R is the average SAR in the rest. An important consequence of how equation ( 14) is constructed is that only one frequency at a time from any working set can maximize such ratio (Zanoli and Trefná 2020). The amplitude of the other frequencies must be set to zero, and the only active frequency is the one whose interference pattern best fits the target shape and location.…”

“…Since the evaluation of the HTQ involves at least one nonlinear step with respect to the complex array steering parameters, EV cannot be directly used to determine the HTQ-optimal solution. A second limitation of EV occurs with multi-frequency optimization: the generalized EV form can not be defined for multiple simultaneous operating frequencies in a conjoint manner (Trefná et al 2017, Zanoli andTrefná 2020).…”

Advanced Radio Frequency Applicators for Thermal Magnetic Resonance Theranostics of Brain Tumors

“…We evaluated the performance of the ThermalMR RF applicators using clinically relevant quality indicators provided by the European Society for Hyperthermic Oncology (ESHO) according to the criteria of characterization of the SAR 10g , index temperature distribution inside TV and hotspots in healthy tissue [ 73 , 91 , 92 , 93 , 94 , 95 , 96 ]. These quality indicators allow the investigation of localized and averaged RF power deposition in the target volume, as well as in remote healthy tissue.…”