* Micromagnetic Analysis as a Way to Evaluate Physical Properties of Magnetic Nanoparticles in Biomedical Applications N. Maniotis and D. Serantes 3
* Physics Department, Aristotle University of Thessaloniki (2022) Physics Department, Aristotle University of Thessaloniki (2022) Thessaloniki, Greece
* MagnaChatr (2022) MagnaChatr, Center for Interdisciplinary Research and Innovation (CIRI-AUTH), 57001 Thessaloniki, Greece
* Applied Physics Department and IIT, Universidade de Santiago de Compostela (2022) 15782 Compostela, Spain
* Correspondence: nimaniot@physics.auth.gr  
Magnetic particle hyperthermia (MPH) is a novel, minimally invasive, therapeutic modality used as a cancer treatment, which employs a magnetic fluid (also termed ferrofluid) as the heating source. A magnetic fluid is a stable colloidal suspension of magnetic nanoparticles (MNPs) that can be injected directly into the tumor or delivered to the tumor via passive or active targeting upon intravenous administration. Once accumulated to the tumor area, MNPs are exposed to an external alternating magnetic field (AMF) that causes a reversal of their magnetic moments, activating mechanisms of energy deposition in the form of heat [1]. The key measure used for characterizing the heating efficiency of nanoparticles in MPH is the specific loss power (SLP), which may be derived from the magnetic hysteresis loop area. In this work, the issue of whether dynamic magnetic properties of a poly-dispersed ferrofluid, modelled using micromagnetic simulations, can be extrapolated to analyse SLP values acquired at high frequencies of excitation fields is addressed. Micromagnetic finite difference simulations were performed using OOMMF software package to obtain the dynamic hysteresis loops under a 24 kA/m AMF amplitude and for various frequencies (50-765 kHz). In OOMMF, finite difference method was used to find the solution of nonlinear Landau-Lifshitz-Gilbert (LLG) equation which describes the precessional motion of nanoparticles magnetization when applying an effective magnetic field [2]. To create a system of randomly oriented nanoparticles having a certain volume fraction, 0.04%, that corresponds to a ferrofluid concentration of 2 mg/mL, we start with a perfect simple cubic lattice with a large lattice spacing so that the particle-particle distance is large enough to neglect dipolar interactions (non-interacting MNPs). The system under study is a set of spherical magnetite nanoparticles of 30 nm with a lognormal size distribution. When the frequency of the applied magnetic field, \(f\), was below ~300 kHz, SLP(\(f\)) followed an exponential increase trend. At this regime, the hysteresis area increases with \(f\) due to the increase in the phase delay in the magnetization response. After a critical \(f\), MNPs magnetization reaches the maximum phase delay (maximum relaxation time of spins) and so any increase in \(f\) leaves the hysteresis area unaffected. To validate our approach, we employed a coupled electromagnetic-thermal model, based on COMSOL Multiphysics simulations that provides an accurate estimation of magnetic field and temperature distribution within the ferrofluid. The time-dependent temperature curves are obtained after 30 minutes of MPH treatment for the same AMF amplitude used in OOMMF simulations (24 kA/m) and for two representative \(f\) values. One at low (200 kHz) and one at high (765 kHz) frequency regime. In each case, the MNPs volumetric power dissipation, imported in heat transfer model to find the temperature curves, is taken equal to the corresponding SLP (\(f\)) value. The numerical MPH curves were found in excellent agreement with the experimental data observed under the same conditions. ## References  
* (1) Rodrigo, I.; Castellanos-Rubio, I.; Garaio, E.; Arriortua, O.K. ; Insausti, M.; Orue, I.; Garcia, J.S. ; Plazaola, F. Exploring the potential of the dynamic hysteresis loops via high field, high frequency and temperature adjustable AC magnetometer for magnetic hyperthermia characterization. _Int. J. Hyperth._**2020**, _37_, 976-991.