Tuning field amplitude to minimise heat-loss variability in magnetic hyperthermia

TL;DR

This work addresses heating heterogeneity in magnetic fluid hyperthermia by examining how shape-induced anisotropy dispersion and AC field amplitude jointly affect single-particle losses. Using real-time LLG dynamics with thermal fluctuations and a macrospin model that combines cubic magnetocrystalline anisotropy with shape-induced uniaxial anisotropy, the authors identify an optimal field amplitude (H_crit) that minimizes the relative dispersion of local losses for larger magnetite nanoparticles (D ≈ 25–30 nm) at clinically relevant frequencies. They show that H_crit depends primarily on particle size and excitation frequency, with only a weak dependence on shape dispersion, though polydispersity increases the overall dispersion and can limit uniform heating. The results provide actionable guidelines for reducing heating heterogeneity in MFH by tuning H_max in concert with synthesis control to achieve shape monodispersity, and they extend previous predictions by incorporating cubic anisotropy and real-time dynamics rather than static, uniaxial models.

Abstract

In this work, we theoretically investigate how shape-induced anisotropy dispersion and magnetic field amplitude jointly control both the magnitude and heterogeneity of heating in magnetite nanoparticle assemblies under AC magnetic fields. Using real time Landau-Lifshitz-Gilbert simulations with thermal fluctuations, and a macrospin model that includes both the intrinsic cubic magnetocrystalline anisotropy and a shape-induced uniaxial contribution, we analyze shape-polydisperse systems under clinically and technologically relevant field conditions. We show that for relatively large particles, around 25 to 30 nm, the relative dispersion of local (single-particle) losses exhibits a well-defined minimum at moderate field amplitudes (between 4 to 12 mT), hence identifying an optimal operating regime that minimizes heating heterogeneity while maintaining substantial power dissipation. The position of this critical field depends mainly on particle size and excitation frequency, and only weakly on shape dispersion, offering practical guidelines for improving heating uniformity in realistic MFH systems.

Figures (10)

• Figure 1: (a) Examples histograms of Gaussian distributions of aspect ratio $r$, centered around the mean $\langle r \rangle=1.1$, for different standard deviations $\sigma_r$, 0.0 (monodisperse) and 0.1 and 0.2. Schematic representations of the corresponding shape-polydisperse ensembles are shown in the upper right corner for illustration purposes. (b) Dependence of the corresponding uniaxial shape anisotropy constant $K_u$ on $r$. The dashed vertical line highlights the mean axial ratio $\langle r \rangle = 1.1$ of the distributions.
• Figure 2: Left axis: Standard deviation of the normalized local hysteresis losses $\sigma_{HL}$, as a function of the normalised applied field amplitude, $H_{max}/\langle{H_A\rangle}$, for a distribution in anisotropy constants $K_u$ of of $\sigma = 0.2$. Right axis: Percentage of this standard deviation in relation to the global normalized hysteresis losses. The $H_{crit}$ value indicates the critical field for minimising dispersion in heat losses. Adapted from Ref. munoz2017towards with permission from the Royal Society of Chemistry.
• Figure 3: Hysteresis loops for $D=25$ nm particles with different aspect ratios $r$. Solid lines correspond to $f=100$ kHz and dashed lines to $f=1000$ kHz, in both cases for $\mu_0 H_{\max}=30$ mT.
• Figure 4: SLP/f vs.$\mu_0 H_{\max}$ for $D=25$ nm particles, for systems with different aspect ratios $r$; for both $f=100$ kHz (solid lines) and $f=1000$ kHz (dashed lines).
• Figure 5: SLP vs.$\mu_0 H_{\max}$ for shape-polydisperse MNPs with $\sigma_r = 0.2$, $f = 1000$ kHz, and $D = 25$ nm. The symbols represent the ensemble-averaged SLP, while the shaded region stands for the standard deviation of SLP, $\sigma_{SLP}$, arising from the distribution of particle shapes. The inset shows the SLP value as a function of $\mu_0 H_{\max}$ for other $\sigma_r$ cases.