Numerical Model for Determining the Magnetic Loss of Magnetic Fluids

Abstract

Magnetic fluid hyperthermia (MFH) is a medical treatment where the temperature in the tissue is increased locally by means of heated magnetic fluid in an alternating magnetic field. In recent years, it has been the subject of a lot of research in the field of Materials, as well as in the field of clinical testing on mice and rats. Magnetic fluid manufacturers aim to achieve three objectives; high heating capacity, biocompatibility and self-regulatory temperature effect. High heating power presents the conversion of magnetic field energy into temperature increase where it is challenging to achieve the desired therapeutic effects in terms of elevated temperature with the smallest possible amount of used material. In order to carry out the therapy, it is primarily necessary to create a fluid and perform calorimetric measurement for determining the Specific Absorption Rate (SAR) or heating power for given parameters of the magnetic field. The article presents a model based on a linear response theory for the calculation of magnetic losses and, consequently, the SAR parameters are based on the physical parameters of the liquid. The calculation model is also validated by calorimetric measurements for various amplitudes, frequencies and shapes of the magnetic field. Such a model can serve to help magnetic fluid developers in the development phase for an approximate assessment of the heating power.

Numerical Investigation of Ferrofluid Preparation during In-Vitro Culture of Cancer Therapy for Magnetic Nanoparticle Hyperthermia

“…This well-known model was implemented and further extended to our problem. The volumetric power p (W/m 3 ) dissipated in a unit volume of MNPs, as well as SLP (W/kg) and ILP (nH∙m 2 /kg) parameters, respectively, were calculated using the following equations [ 42 , 45 , 46 , 61 ]: where μ 0 = 4π∙10 −7 H/m represents the permeability of free space, H (A/m) is the AMF strength, f (Hz) is the frequency of the magnetic field, χ ’’ is the out-of-phase component of the complex magnetic susceptibility χ = χ ’ − j χ ’’ for the MF, c MNPs (mg/mL) is the concentration of nanoparticles, and ϕ v MNPs stands for the volume fraction of MNPs in the sample. The imaginary part of the complex magnetic susceptibility can be expressed as [ 46 , 62 ]: where χ 0 represents the static equilibrium magnetic susceptibility, and τ (s) is the effective relaxation time.…”

“…The initial slope method is commonly used to empirically determine the heat losses in magnetic fluid (MF). The following expression can be used to find the SLP and ILP values [ 43 , 45 , 48 ]: where m MF and C MF (J/kg/K) represent the mass and specific heat capacity of the magnetic fluid, respectively. Moreover, m MNPs (kg) is the mass of MNPs, and Δ T/ Δ t (K/s) corresponds to the temperature increment calculated for the initial 20 s of AMF exposure [ 7 , 48 ].…”

“…Hence, the thermo-physical properties of the aqueous suspension of MNPs depend on the individual properties of the constituents of the MF sample. The expressions for the effective ferrofluid properties, such as their density ρ MF (kg/m 3 ), specific heat capacity C MF (J/kg/K), thermal conductivity k MF (W/m/K), and viscosity η MF (Pa∙s), respectively, are given by [ 43 , 45 , 48 , 64 , 65 ]: where ϕ v H2O and ϕ m H2O are the volume and mass fractions of water, respectively, and ϕ v H2O represents the mass fraction of MNPs immersed in aqueous solution. Table 2 summarizes the individual and combined thermo-physical properties of the magnetite MNPs, water, ferrofluid sample, and polystyrene tube, respectively.…”

“…The induction heating of MNPs exposed to an applied magnetic field (AMF) is specified as the specific loss power (SLP), also called the specific absorption rate (SAR) [ 42 , 43 , 44 ], which is a quantity that evaluates the efficiency of nanoparticles in transforming EM energy into power. The SLP can be calculated by calorimetric and magnetic methods [ 7 , 45 , 46 ]. It has been recorded that the SLP values are influenced by multiple parameters of the calorimetric setup, such as the volume of the MF sample, the shape of the Eppendorf tube, the thermo-physical properties of the ferrofluid system, the position of the temperature sensor, and the external conditions [ 26 , 47 , 48 ].…”

Development of a Magnetic Fluid Heating FEM Simulation Model with Coupled Steady State Magnetic and Transient Thermal Calculation

“…In the literature [7], the authors deal with the development of the analytical relationship and computations of power dissipation in magnetic fluid in an alternating magnetic field based on relaxation processes in the magnetic fluid. Similarly, article [8] presents a model based on relaxation processes to calculate magnetic losses and SAR based on the parameters of the magnetic fluid. The model was validated with the use of calorimetric measurements for different magnetic field amplitudes, frequencies and shapes.…”