Detailed calculations of the specific absorption rate (SAR) of a dilute assembly of iron oxide nanoparticles with effective uniaxial anisotropy dispersed in a liquid are performed depending on the particle diameters, the alternating (ac) magnetic field amplitude H0 and the liquid viscosity. For small and moderate H0 values with respect to particle anisotropy field Hk the SAR of the assembly as a function of the particle diameter passes through a characteristic maximum and then reaches a plateau, whereas for sufficiently large amplitudes, H0 ~ Hk, the SAR increases monotonically as a function of diameter. The realization of viscous and magnetic oscillation modes for particle unit magnetization vector and director for moderate and sufficiently large H0 values, respectively, explains this behavior. It is found that the SAR of the assembly changes inversely with the viscosity only in a viscous mode, for nanoparticles of sufficiently large diameters. In the magnetic mode the SAR of the assembly is practically independent of the viscosity, since in this case the nanoparticle director only weakly oscillates around the ac magnetic field direction. The conditions for the validity of the linear response theory have been clarified by comparison with the numerical simulation data.

A linear combination of spherically symmetric heat sources is shown to provide optimal stationary thermal distribution in magnetic hyperthermia. Furthermore, such spatial location of heat sources produces suitable temperature distribution in biological medium even for assemblies of magnetic nanoparticles with a moderate value of specific absorption rate (SAR), of the order of 100–150 W/g. We also demonstrate the advantage of using assemblies of spherical magnetic nanocapsules consisting of metallic iron nanoparticles covered with non magnetic shells of sufficient thickness in magnetic hyperthermia. Based on numerical simulation we optimize the size and geometric structure of biocompatible spherical capsules in order to minimize the influence of strong magneto-dipole interaction between closely spaced nanoparticles. It is shown that assembly of capsules can provide sufficiently high SAR values of the order of 250–400 W/g at moderate amplitudes H0 = 50–100 Oe and frequencies f = 100–200 kHz of alternating magnetic field, being appropriate for application in clinics.

The dynamics of magnetic nanoparticles in a viscous liquid in a rotating magnetic field has been studied by means of numerical simulations and analytical calculations. In the magneto-dynamics approximation three different modes of motion of the unit magnetization vector and particle director are distinguished depending on frequency and amplitude of the rotating magnetic field. The specific absorption rate of a dilute assembly of superparamagnetic nanoparticles in rotating magnetic field is calculated by solving the Landau–Lifshitz stochastic equation for the unit magnetization vector and the stochastic equation for the particle director. At elevated frequencies an optimal range of particle diameters is found where the specific absorption rate of an assembly in a rotating magnetic field has a maximum. It is shown that with an optimal choice of the particle sizes sufficiently large SAR values of the order of 400–500 W/g can be obtained in a rotating magnetic field with a frequency f = 400 kHz and a moderate magnetic field amplitude H 0 = 100 Oe.

A linear combination of spherically symmetric heat sources is shown to provide optimal stationary thermal distribution in magnetic hyperthermia. Furthermore, such spatial location of heat sources produces suitable temperature distribution in biological medium even for assemblies of magnetic nanoparticles with a moderate value of specific absorption rate (SAR), of the order of 100 - 150 W/g. We also demonstrate the advantage of using assemblies of magnetic nanocapsules consisting of metallic iron nanoparticles covered with non magnetic shells of sufficient thickness in magnetic hyperthermia. Based on numerical simulation we optimize the size and geometric structure of biocompatible capsules in order to minimize the influence of strong magneto-dipole interaction between closely spaced nanoparticles. It is shown that assembly of capsules can provide sufficiently high SAR values of the order of 250 - 400 W/g at moderate amplitudes H0·= 50 - 100 Oe and frequencies f = 100 - 200 kHz of alternating magnetic field, being appropriate for application in clinics.