Computation of ultimate SAR amplification factors for radiofrequency hyperthermia in non-uniform body models: impact of frequency and tumour location

Abstract

Purpose We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume. Methods First, we generate a basis-set of solutions to Maxwell’s equations inside the body model. We place a large number of electric and magnetic dipoles around the body model and excite them with random amplitudes and phases. We then compute the electric fields created in the body model by these excitations using an ultra-fast volume integral solver called MARIE. We express the field pattern that maximises the SAF in the target tumour as a linear combination of these basis fields and optimise the combination weights so as to maximise SAF (concave problem). We compute the uSAFs in the Duke body models at 10 frequencies in the 20–900 MHz range and for twelve 3 cm-diameter tumours located at various depths in the head and neck. Results For both shallow and deep tumours, the frequency yielding the greatest uSAF was ~900 MHz. Since this is the greatest frequency that we simulated, we hypothesise that the globally optimal frequency is actually above that. Conclusions The uSAFs computed in this work are very large (40–100 for shallow tumours and 4–17 for deep tumours), indicating that there is a large room for improvement of the current state-of-the-art head and neck HT devices.

The ultimate intrinsic signal‐to‐noise ratio of loop‐ and dipole‐like current patterns in a realistic human head model

“…Several methods have been proposed to calculate the UISNR: Use a linear combination of plane waves impinging on the sample and solve the scattering problem Randomly excite a large number of elementary electric and magnetic dipoles lying on a Huygen's surface and solve the Helmholtz equation Use the analytically known eigenfunctions of the Helmholtz operator in spherical or cylindrical coordinate systems.…”

Wideband Self‐Grounded Bow‐Tie Antenna for Thermal MR

“…For example, a well‐established implementation of the fractionated dipole uses a housing with a size of ~ 300 x 40 x 20 mm 3 ; our compact SGBT configuration results in a volume reduction of 52% compared with this, and a reduction in the antenna length of nearly a factor of three . The compact size of the RF antenna building block and its low nearest neighbor coupling is suitable for high‐density and many‐element RF array configurations, which is crucial for improving the focal point quality of thermal interventions and for approaching the ultimate SAR amplification factors predicted by numerical simulations …”

“…Further to 19 F and 1 H imaging, the SGBT antenna building block supports RF‐induced heating for a broad frequency range. Arranged in an RF array, this feature facilitates the adjustment of the thermal intervention frequency, providing an extra degree of freedom to the thermal intervention . The proton‐based MR thermometry has the potential to acquire three‐dimensional temperature maps, enabling a feedback loop to control RF power deposition during a thermal intervention .…”

“…Ensuring a patient‐ and problem‐oriented adaptation of the size, uniformity and location of the RF energy deposition in the target region is highly relevant for the thermal intervention, with the focal point quality being governed by the radiation pattern of the single RF transmit element, the RF channel count and the thermal intervention radiofrequency of the RF applicator . Reports on the radiation pattern of resonant structures underline the benefits of dipole antenna arrays for enhancing the focal point quality in thermal interventions .…”

“…Theoretical research and numerical simulations of targeted RF heating have shown how an ultrahigh field MR (UHF‐MR) instrument can be adapted to generate highly focused heat in regions of tissue by the use of RF antenna arrays . Studies on ultimate intrinsic specific absorption rate (SAR) and RF applicator concepts suggested high frequencies of up to 1 GHz for a highly focused EM energy deposition . Antenna count and positioning also influence the focal point quality .…”