IRM supervised the design of the study. FJA led the design of the study and helped to draft the manuscript. All authors read and approved the final manuscript.”

“Background Magnetic

nanoparticles are a topic of growing interest because of their versatile applications such as drug delivery, SN-38 cell line magnetic hyperthermia, magnetic separation, magnetic resonance imaging (MRI) contrast enhancement, and ultrahigh-density data ROCK inhibitor storage [1–14]. Among those, magnetic hyperthermia is a novel therapeutic method in which the magnetic nanoparticles are subjected to an alternating magnetic field to generate a specific amount of heat to raise the temperature of a tumor to about 42°C to 46°C at which certain mechanisms of cell damage are activated [15, 16]. These mechanisms which produce heat in alternating current (AC) magnetic fields include the following: (1) hysteresis, (2) Neel or Brownian relaxation, and (3) viscous losses [17]. The generated heat is quantitatively described by the specific absorption rate (SAR) Cl-amidine in vivo of nanoparticles which is related to specific loss per cycle of hysteresis loop (A) by the equation SAR = A × f in which f is the frequency of the applied field. There are four models based on size regimes to describe the magnetic properties of nanoparticles [17]: 1. At superparamagnetic

size regime in which the hysteresis area is null, the equilibrium functions are used. In this size range depending on the anisotropy energy, the magnetic behavior of nanoparticles progressively changes from the Langevin function (L(ξ) = coth(ξ) - 1/ξ) for zero anisotropy to tanh(ξ) for maximal anisotropy where ξ = (μ 0 M s VH max)/(k B T). 2. Around the superparamagnetic-ferromagnetic transition size, the linear response theory (LRT) does the job for

us. The LRT is a model for describing the dynamic magnetic properties of an assembly of nanoparticles using the Neel-Brown relaxation time and assumes a linear relation between PtdIns(3,4)P2 magnetization and applied magnetic field. The area of the hysteresis loop is determined by [17] (1) where σ = KV/k B T, ω = 2πf, and τ R is the relaxation time of magnetization which is assumed to be equal to the Neel-Brown relaxation time (τ N). 3. In the single-domain ferromagnetic size regime, the Stoner-Wohlfarth (SW)-based models are applied which neglect thermal activation and assume a square hysteresis area that is practically valid only for T = 0 K or f → ∞ but indicates the general features of the expected properties for other conditions. Based on the SW model for magnetic nanoparticles with their easy axes randomly oriented in space, the hysteresis area is calculated by [17] (2) 4. Finally, for multi-domain ferromagnetic nanoparticles, there is no simple way to model the magnetic properties of such large nanoparticles. In hyperthermia experiments, increasing the nanoparticle size to multi-domain range promotes the probability of precipitation of nanoparticles which leads to the blockage of blood vessels.