Influence of size, volume concentration and aggregation state on magnetic nanoparticle hyperthermia properties versus excitation conditions

Abstract

Treatment planning in magnetic hyperthermia requires a thorough knowledge of specific loss power of magnetic nanoparticles as a function of size and excitation conditions. Moreover, in biological tissues the magnetic nanoparticles can aggregate into clusters, making the evaluation of their heating performance more challenging because of the magnetostatic dipole–dipole interactions. In this paper, we present a comprehensive modelling analysis of 10–40 nm sized spherical magnetite (Fe₃O₄) nanoparticles, investigating how their heating properties are influenced by magnetic field parameters (peak amplitude and frequency), and by volume concentration and aggregation state. The analysis is performed by means of an in-house micromagnetic numerical model, which solves the Landau–Lifshitz–Gilbert equation under the assumption of single-domain nanoparticles, including thermal effects via a Langevin approach. The obtained results provide insight into how to tune hyperthermia properties by varying magnetic nanoparticle size, under different excitation magnetic fields fulfilling the Hergt–Dutz limit (frequency between 50 kHz and 1 MHz, and peak amplitude between 1 kA m⁻¹ and 50 kA m⁻¹). Special attention is finally paid to the role of volume concentration and aggregation order, putting in evidence the need for models able to account for stochasticity and clustering in spatial distribution, to accurately simulate the contribution of magnetostatic dipole–dipole interactions in real applications.