Unified model of hyperthermia via hysteresis heating in systems of interacting magnetic nanoparticles

Abstract

We present a general study of the frequency and magnetic field dependence of the specific heat power produced during field-driven hysteresis cycles in magnetic nanoparticles with relevance to hyperthermia applications in biomedicine. Employing a kinetic Monte-Carlo method with natural time scales allows us to go beyond the assumptions of small driving field amplitudes and negligible inter-particle interactions, which are fundamental to the applicability of the standard approach based on linear response theory. The method captures the superparamagnetic and fully hysteretic regimes and the transition between them. Our results reveal unexpected dipolar interaction-induced enhancement or suppression of the specific heat power, dependent on the intrinsic statistical properties of particles, which cannot be accounted for by the standard theory. Although the actual heating power is difficult to predict because of the effects of interactions, optimum heating is in the transition region between the superparamagnetic and fully hysteretic regimes.

The Néel Magnetic Relaxation Dynamics in Nanoparticle Systems - Phenomenological Approach versus Stochastic Approach

“…In many of these models, we can find stochastic or phenomenological approaches. For example, one of the most updated models, based on the KMC method (kinetic Monte Carlo method), uses a stochastic approach [20]. Thus, for effective local magnetic fields of particles whose density is lower than a critical value, there are two equilibrium nanoparticle states, "+" and "−", and the probability of a nanoparticle to switch between these states is P i = 1 − exp(−t/τ i ).…”

“…Both models took into account the dipole-dipole interaction, but achieved conflicting results. To these models, we can add many studies carried out using the Monte Carlo stochastic methods [18][19][20], or the numerical solution of the Landau-Lifshitz-Gilbert stochastic differential equation (LLG equation) [21], or rigorous analytical models [22,23]. Unfortunately, they could offer only approximate solutions, or solutions for weak magnetic dipole interactions.…”

Specific Absorption Rate of Assembly of Magnetite Nanoparticles with Cubic Magnetic Anisotropy

“…The numerical simulations are performed by solving stochastic Landau-Lifshitz (LL) equation [7][8][9]. This approach takes into account both thermal fluctuations of the particle magnetic moments and strong magnetodipole interaction [10][11] in assemblies of dense fractal-like aggregates of nanoparticles. It has been discovered recently [12] that fractal clusters of nanoparticles originate in biological cells loaded with magnetic nanoparticles.…”

Studies on Approximation Methods in Calculating the Magnetic Dipolar Interaction Energy, and Its Impact on the Relaxation Time of Magnetic Nanoparticle Systems

“…The simulation models offer an efficient simulation scheme and have the major advantage to rigorously treat the local and temporal fluctuations of the macroscopic quantities characterizing the system. The mostly used simulation methods are Monte Carlo [10][11][12] and the magnetization dynamics [4]. Between theoretical and simulation models, we can set the so-called stochastic-phenomenological models [13][14][15][16].…”