Spatially focused magnetic hyperthermia: comparison of MRSh and sLLG equations

TL;DR

This work addresses spatially localized heating in magnetic nanoparticle hyperthermia by directly comparing Brownian (MRSh) and Néel (sLLG) relaxation models through magnetic and ordinary viscosity. By mapping energy loss and localization metrics (SAR/ILP) between the two frameworks, the authors demonstrate that the sLLG equation can reproduce the MRSh results with suitable parameter choices, validating a unified description across relaxation regimes. A key finding is that perpendicular AC and DC field configurations yield superior spatial focusing at low frequencies, a regime relevant to image-guided therapy with MPI, while high-frequency behavior converges for both geometries. The results support using perpendicular field geometries in MPI-guided hyperthermia and provide a practical bridge between Brownian and Néel descriptions for designing spatially targeted nanoparticle heating protocols.

Abstract

Magnetic hyperthermia with metallic nanoparticles is a therapeutic strategy that relies on heating cancer cells to levels sufficient to damage or destroy them. After injection, the nanoparticles accumulate in tumor tissues, where they transfer energy from the applied time-dependent magnetic field to the surrounding medium, thereby increasing the local temperature. This heating effect can be spatially focused (superlocalized) by combining AC and DC magnetic fields. Heat generation arises either from the rotation of the particle or from the rotation of its magnetic moment. The theoretical framework is provided by the Martsenyuk-Raikher-Shliomis (MRSh) equation for the former and the stochastic Landau-Lifshitz-Gilbert (sLLG) equation for the latter. However, by using the concept of magnetic and ordinary viscosity, the results of these approaches can be directly compared, which is our goal in this work, with special emphasis on their ability to achieve spatial localization. On the basis of this comparison, we propose the use of perpendicular AC and DC magnetic fields for image-guided thermal therapy with magnetic particle imaging.

Figures (7)

• Figure 1: (Color online.) Spatial focusing is shown by plotting SAR values as a function of the DC field which is in parallel combination of the AC magnetic field. The lower panel is for lower frequencies suitable for MPI and on the upper panel one finds higher frequencies needed for magnetic hyperthermia. The AC field strength is chosen to be 30 mT.
• Figure 2: (Color online.) Dynamical hysteresis loops are given for various angular frequencies of the applied AC magnetic field while its amplitude (field strength) is fixed. The left column stands for larger frequencies needed for magnetic hyperthermia and on the right column one finds smaller frequency values used in MPI. The static DC field amplitude is increased from top to bottom.
• Figure 3: Results obtained by the sLLG equation (for field strength 1kA/m and frequencies $5 \times 10^7$ Hz to the top and $10^6$ Hz to the bottom). This can be compared to Fig. \ref{['fig1']} given by the MRSh approach. One finds similar bell-shapes for the SAR/ILP values.
• Figure 4: (Color online.) Dynamical hysteresis loops obtained by the sLLG equation which are similar to the dynamical hysteresis loops of Fig. \ref{['fig2']} given by the MRSh method.
• Figure 5: (Color online.) Dynamic hysteresis loop (for parallel combination (\ref{['para']})) and spatial focusing of SAR values for parallel (\ref{['para']}) and perpendicular (\ref{['perp']}) combinations) obtained by the sLLG method for field strength 1kA/m and frequency $5 \times 10^7$ Hz. One finds no difference in the spatial focusing ability of parallel and perpendicular orientation of AC and DC fields.