Magnetic nanoparticles clustering effects on the temperature field in magnetic hyperthermia

Magnetic hyperthermia is a medical technique based on the generation of therapeutic heat by a magnetic nanoparticle (MNP) system in the presence of a high-frequency electromagnetic field. The temperature developed in the tumoral tissue and the overall heating efficiency strongly depend on the magnetic field parameters (frequency and amplitude), as well as on the intrinsic properties of the MNPs. Nanoparticle clustering due to interparticle dipolar interactions plays an important role in the relaxation dynamics and significantly modifies the energy barriers involved in the Néel–Brown relaxation processes. In this work, the influence of interparticle spacing αnm, particle size dpnm, and crystalline anisotropy constant KJ/m3 on the Specific Absorption Rate (SAR) was analyzed using theoretical models that include dipolar interaction effects. Two relaxation scenarios were considered: the Dormann model, where the dipolar coupling increases the effective energy barrier, and the Mørup model, in which the effective barrier is reduced. The results reveal distinct behaviors of SAR: In the Dormann case SAR1, strong dipolar interactions within the cluster enhance the barrier and produce the maximum SAR for moderate α and K values, followed by a decrease toward a plateau at large interparticle distances. In contrast, the Mørup case SAR2 shows a monotonic increase in the SAR with particle dispersion, stabilizing when interparticle coupling becomes negligible. The optimal therapeutic range was found near dp≈17−18nm, where Néel relaxation is most efficient. Numerical simulation performed using COMSOL Multiphysics demonstrated that the spatial temperature distribution and the thermal damage of the tumoral tissue closely follow the SAR trends: Dormann-related heating Q1 produces higher local temperatures, while Mørup-related heating Q2 leads to smoother but less intense thermal profiles. In addition, the influence of carrier-fluid viscosity on the temperature rise is minimal, confirming the dominance of Néel relaxation in the investigated parameter range. These results show that controlling the particle arrangement, interparticle distance, and magnetic anisotropy enables tunable modulation of energy barriers and heating efficiency, providing valuable guidelines for optimizing nanoparticle-based agents in magnetic hyperthermia.