Brownian Relaxation Time Research Articles

Improvements of magnetic nanoparticle assays for SARS-CoV-2 detection using a mimic virus approach

Immunoassays with magnetic nanoparticles (MNPs) as markers are a promising approach for the fast and sensitive virus detection. Upon binding of antibody-functionalized MNP on virus proteins, the hydrodynamic diameter increases and a change in the Brownian relaxation time can be measured. In this study, we detect the whole SARS-CoV-2 by mimicking it with streptavidin-coated polystyrene beads with biotinylated spike proteins. Changes of the MNP dynamics are measured by alternating current susceptometry and magnetic particle spectroscopy. Due to the multiple binding sites of MNP and virus, crosslinking enlarges the change of the hydrodynamic diameter. In order to improve the sensitivity and the limit of detection of the assay, the ratio of the virus to the MNP amount RMV/MNP is investigated in detail. High RMV/MNP ratios lead to a saturation of the MNPs with viruses, so that the cluster size and therefore the sensitivity decrease again. Additionally, it is found that the smallest virus concentrations can be detected for small MNP concentrations. It is also shown that the RMV/MNP range that can be used for an unambiguous detection of viruses depends on the virus/MNP concentration; it shifts with increasing MNP concentration to smaller RMV/MNP values. For very small virus concentrations, an increase of the Brownian relaxation time is detected implying a decrease of the hydrodynamic diameter. Furthermore, the optimal antibody concentration for MNP functionalization was determined. It is also found that a washing process with a centrifuge improves the sensitivity by reliably removing unbound antibodies and eliminating small MNPs with improper functionalization.

Feature Matching of Microsecond-Pulsed Magnetic Fields Combined with Fe3O4 Particles for Killing A375 Melanoma Cells.

The combination of magnetic fields and magnetic nanoparticles (MNPs) to kill cancer cells by magneto-mechanical force represents a novel therapy, offering advantages such as non-invasiveness, among others. Pulsed magnetic fields (PMFs) hold promise for application in this therapy due to advantages such as easily adjustable parameters; however, they suffer from the drawback of narrow pulse width. In order to fully exploit the potential of PMFs and MNPs in this therapy, while maximizing therapeutic efficacy within the constraints of the narrow pulse width, a feature-matching theory is proposed, encompassing the matching of three aspects: (1) MNP volume and critical volume of Brownian relaxation, (2) relaxation time and pulse width, and (3) MNP shape and the intermittence of PMF. In the theory, a microsecond-PMF generator was developed, and four kinds of MNPs were selected for in vitro cell experiments. The results demonstrate that the killing rate of the experimental group meeting the requirements of the theory is at least 18% higher than the control group. This validates the accuracy of our theory and provides valuable guidance for the further application of PMFs in this therapy.

Field-dependent Néel relaxation time of magnetic nanoparticles in AC excitation fields: Boundary field between Néel- and Brownian-dominant regions

We investigated the field-dependent Néel relaxation time of magnetic nanoparticles (MNPs) in an AC excitation field. Specifically, a fundamental component of the magnetization for immobilized MNPs was studied by numerical simulation while changing the frequency f and amplitude Hac of the field. From the simulation results, we clarified the Hac dependence of the effective Néel relaxation time τN,e and obtained an empirical expression for τN,e(Hac) for the first time. The expression was obtained for the cases when the angle of the easy axis of magnetization in MNPs is fixed and randomly distributed. Using the Hac dependencies of τN,e and the previously reported Brownian relaxation time τB,e, we showed that the behavior of suspended MNPs changes from Brownian-dominant to Néel-dominant when Hac increases, even when the MNP parameters are fixed, and we obtained an expression for the boundary field between them. Furthermore, we classified several types of responses for the suspended MNPs in the AC field using the magnitude relationship among τN,e(Hac), τB,e(Hac), and 1/(2πf). Finally, we experimentally verified the classification, and reasonable agreement was observed between the experiment and analysis. The results are useful for determining suitable MNP parameters and excitation conditions for various biomedical applications.

A nudge over the relaxation plateau: effect of pH, particle concentration, and medium viscosity on the AC induction heating efficiency of biocompatible chitosan-coated Fe3O4 nanoparticles

The effects of pH, MNP concentration, and medium viscosity on the magnetic fluid hyperthermia (MFH) properties of chitosan-coated superparamagnetic Fe3O4 nanoparticles (MNPs) are probed here. Due to the protonation of the amide groups, the MNPs are colloidally stable at lower pH (∼2), but form aggregates at higher pH (∼8). The increased aggregate size at higher pH causes the Brownian relaxation time (τ B) to increase, leading to a decrease in specific absorption rate (SAR). For colloidal conditions ensuring Brownian-dominated relaxation dynamics, an increase in MNP concentrations or medium viscosity is found to increase the τ B. SAR decreases with increasing MNP concentration, whereas it exhibits a non-monotonic variation with increasing medium viscosity. Dynamic hysteresis loop-based calculations are found to be in agreement with the experimental results. The findings provide a greater understanding of the variation of SAR with the colloidal properties and show the importance of relaxation dynamics on MFH efficiency, where variations in the frequency-relaxation time product across the relaxation plateau cause significant variations in SAR. Further, the in vitro cytotoxicity studies show good bio-compatibility of the chitosan-coated Fe3O4 MNPs. Higher SAR at acidic pH for bio-medically acceptable field parameters makes the bio-compatible chitosan-coated Fe3O4 MNPs suitable for MFH applications.

Recognition of rotational modes of magnetic nanoparticles by frequency dependence of magnetic linear dichroism under AC field

This study shows that magnetic linear dichroism (MLD) measurement has great potential for characterizing magnetic nanoparticles (MNPs) used in recently developing biomedical applications or nanoscale mechanical measurement techniques. MLD of MNP suspension reflects the orientation of the MNP. We investigated the frequency dependence of the MLD of MNP suspension under a simple AC field and the effect of the MNP size and material. Under an AC field with the frequency f, the MLD oscillated with 2f for every MNP. The amplitude and phase of this 2f-oscillation were precisely measured with a lock-in amplifier, and we showed the MLD2f frequency spectrum, a plot of real and imaginary parts of the 2f-component of MLD as a function of f. We found that the shape of the MLD2f frequency spectrum can distinguish the rotational modes of MNPs in an AC field. Therefore, this spectrum is helpful for the selection of MNPs for each technique mentioned above. We propose two model functions to fit the MLD2f frequency spectra, consistent with each rotational mode. It is shown that one of the fitting parameters τ0 is associated with the rotational Brownian relaxation time of MNP, and the other parameter β would represent the distribution of the anisotropy energy. The frequency dependence of MLD will provide precise insights into the magnetization and orientational dynamics of the MNP in liquid.

Estimation of biomolecule amount by analyzing magnetic nanoparticle cluster distributions from alternating current magnetization spectra for magnetic biosensing

The hydrodynamic size distribution of magnetic nanoparticle (MNP) clusters is crucial for determining the amounts of biomolecules by analyzing the distributions of the Brownian relaxation time in the corresponding alternating current (AC) magnetization spectra. This study proposes a method for estimating the distribution of MNP clusters from recorded AC magnetization spectra using an experimental-based model. The proposed model is used to form a matrix equation that comprises the distribution and AC magnetization spectra of MNP clusters, and the MNP–biomolecule cluster distribution is obtained by solving an inverse problem. The results show that the variations in the MNP clusters distribution estimated from the model correspond to those measured by dynamic light scattering. The MNP cluster distributions estimated using the experimental model were used to estimate streptavidin concentrations in the range of 0.19–3.38 μM. The estimated values agree accurately with the true values, demonstrating the feasibility of the proposed method for biosensing.

A study of Brownian relaxation time in magnetic nanofluids: a semi-analytical model

A study of Brownian relaxation time in magnetic nanofluids: a semi-analytical model

Relaxation spectral analysis in multi-contrast vascular magnetic particle imaging.

Magnetic nanoparticles (MNPs) are used as tracers without ionizing radiation in vascular imaging, molecular imaging, and neuroimaging. The relaxation mechanisms of magnetization in response to excitation magnetic fields are important features of MNPs. The basic relaxation mechanisms include internal rotation (Néel relaxation) and external physical rotation (Brownian relaxation). Accurate measurement of these relaxation times may provide high sensitivity for predicting MNP types and viscosity-based hydrodynamic states. It is challenging to separately measure the Néel and Brownian relaxation components using sinusoidal excitation in conventional MPI. We developed a multi-exponential relaxation spectral analysis method to separately measure the Néel and Brownian relaxation times in the magnetization recovery process in pulsed vascular MPI. Synomag-D samples with different viscosities were excited using pulsed excitation in a trapezoidal-waveform relaxometer. The samples were excited at different field amplitudes ranging from 0.5 to 10 mT at intervals of 0.5 mT. The inverse Laplace transform-based spectral analysis of the relaxation-induced decay signal in the field-flat phase was performed by using PDCO, a primal-dual interior method for convex objectives. Néel and Brownian relaxation peaks were elucidated and measured on samples with various glycerol and gelatin concentrations. The sensitivity of viscosity prediction of the decoupled relaxation times was evaluated. A digital vascular phantom was designed to mimic a plaque with viscous MNPs and a catheter with immobilized MNPs. Spectral imaging of the digital vascular phantom was simulated by combining a field-free point with homogeneous pulsed excitation. The relationship between the Brownian relaxation time from different tissues and the number of periods for signal averages was evaluated for a scan time estimation in the simulation. The relaxation spectra of synomag-D samples with different viscosity levels exhibited two relaxation time peaks. The Brownian relaxation time had a positive linear relationship with the viscosity in the range 0.9 to 3.2 mPa · s. When the viscosity was >3.2 mPa · s, the Brownian relaxation time saturated and did not change with increasing viscosity. The Néel relaxation time decreased slightly with an increase in the viscosity. The Néel relaxation time exhibited a similar saturation effect when the viscosity level was >3.2 mPa · s for all field amplitudes. The sensitivity of the Brownian relaxation time increased with the field amplitude and was maximized at approximately 4.5 mT. The plaque and catheter regions were differentiated from the vessel region in the simulated Brownian relaxation time map. The simulation results show that the Néel relaxation time was 8.33±0.09 μs in the plaque region, 8.30±0.08 μs in the catheter region, and 8.46±0.11 μs in the vessel region. The Brownian relaxation time was 36.60±2.31 μs in the plaque region, 30.17±1.24 μs in the catheter region, and 31.21±1.53 μs in the vessel region. If we used 20 excitation periods for image acquisition in the simulation, the total scan time of the digital phantom was approximately 100 s. Quantitative assessment of the Néel and Brownian relaxation times through inverse Laplace transform-based spectral analysis in pulsed excitation, highlighting their potential for use in multi-contrast vascular MPI.

Simultaneous estimation of magnetic moment and Brownian relaxation time distributions of magnetic nanoparticles based on magnetic particle spectroscopy for biosensing application.

Magnetic nanoparticles (MNPs) exhibit unique physicochemical characteristics owing to their comparable dimensions with important biological substances, high surface-to-volume ratios, size-dependent magnetic properties, and temperature sensitivity. In this study, we present a novel method for simultaneously estimating the magnetic moment and Brownian relaxation time distribution of MNPs based on AC magnetization harmonics. We provide a detailed description of the theoretical framework and experimental procedures. The dynamics of MNP magnetization are described using the Fokker-Planck equation, and a matrix equation is established to connect the magnetic moment, Brownian relaxation time, and magnetization harmonics. By employing a non-negative linear least squares algorithm with constraints, the magnetic moment and Brownian relaxation time distributions are inversed, which are then converted into the distributions of core sizes and hydrodynamic sizes. Finally, the estimated core size distribution reconstructed from M-H curves is consistent with the hydrodynamic size distribution measured by dynamic light scattering. This method is particularly useful for facilitating quantitative magnetic immunoassays.

Nonlinear response of a dilute ferrofluid to an alternating magnetic field

The response of dilute monodisperse ferrofluid to alternating magnetic field is studied theoretically. Brownian rotational relaxation of magnetic nanoparticles is taken into account. Susceptibilities of magnetization harmonics are calculated in a wide range of field amplitudes and frequencies via three common approaches: the Fokker-Planck equation for the one-particle orientation distribution function, the Martsenyuk-Raikher-Shliomis effective field method and the Langevin dynamics simulation which is based on direct numerical integration of particles’ stochastic equations of motion. A comparison of these approaches revealed that all of them are able to describe accurately the behavior of the fundamental magnetization harmonic in a broad range of field parameters. But in the case of high-order harmonics, shortcomings of Langevin dynamics and the effective field method manifest themselves. Due to strong random fluctuations of the system magnetization, Langevin dynamics fails to produce reliable results in the weak-field limit, i.e. when the characteristic magnetic energy scale is lower than the system thermal energy. The Martsenyuk-Raikher-Shliomis equation gives a large systematic error for high-order harmonics if the field period is comparable with (or smaller than) the Brownian relaxation time.

Empirical and simulated evaluations of easy-axis dynamics of magnetic nanoparticles based on their magnetization response in alternating magnetic field

Physical rotation of the easy axes of magnetic nanoparticles significantly affects their magnetization properties in fluid, which are important for biomedical applications. The rotation and alignment of the easy axis toward a specific direction in an alternating magnetic field are affected by fluid conditions such as viscosity, the condition of the applied magnetic field, and the magnetic properties of the nanoparticles, including anisotropy. In this study, we experimentally evaluated the physical rotation and alignment of the easy axes of nanoparticles in a viscous medium by preparing samples in which the orientation of the easy axis was fixed in an alternating field at each frequency across a wide frequency range. The numerical simulation with respect to the transitional and steady-state easy-axis dynamics determined by Néel and Brownian relaxation sufficiently supported the empirically observed phenomena. The factors dominating the easy-axis dynamics with rotation and static orientation in an alternating magnetic field, such as the Brownian relaxation time, magnetic torque, and applied field frequency, were clarified. The alignment degree, including its direction and rotation amplitude, was found to depend on the viscosity of the medium associated with the Brownian regime and the magnetic torque derived from the Néel regime. Nonlinear magnetization appeared as the harmonic components of the magnetization in a viscous medium were strongly influenced by the static alignment of the easy axis.

Heating loss mechanism in β-NaFeO2 nanoparticles for cancer treatment under alternating field

The induction heating loss mechanism in nanofluids prepared using synthesized β-NaFeO2 nanoparticles has been discussed concerning optimization of magnetic relaxation (Neel and Brownian) losses, specific absorption rate (SAR), intrinsic loss power (ILP)as well as the concentration of nanoparticles. The highest value of SAR for β-NaFeO2 nanoparticles is 705.86 W/g at 335.2 Oe field and 267 kHz frequency. The value of Brownian and total relaxation time has been calculated theoretically and found to be τB= 6.126 × 10−4 sand τ = 2.668 × 10−7 s, respectively. For Hyperthermia treatment, 2 to 5 mg/mL is the best suitable lowest concentration to achieve high SAR and ILP under applied field. The maximum value of ILP observed is 1.49 nHm2/kg. The calculated theoretical and experimental parameters of induction heating make synthesized β-NaFeO2 nanoparticles suitable for the treatment of cancer via Hyperthermia.

Magnetic hyperthermia studies in magnetite ferrofluids based on bio-friendly oils extracted from Calophyllum inophyllum, Brassica juncea, Ricinus communis and Madhuca longifolia

We study the magnetic hyperthermia efficiency of magnetite ferrofluids based on bio-friendly oils extracted from Calophyllum inophyllum (punnaga), Brassica juncea (mustard), Ricinus communis (castor) and Madhuca longifolia (iluppai) seeds. Reported medicinal uses of these bio-friendly oils make them interesting candidates for hyperthermia from a perspective of topical skin applications. Magneto-caloric experiments are performed at a fixed frequency of 126 kHz and varying field amplitudes of 33.1–25.7 kA/m. Experimental findings show that field induced heating efficiency is the highest for the punnaga oil based ferrofluids (~170.0 ± 8.2 W/gFe) and the estimated intrinsic loss power of ~ 1.26 nHm2kg−1 is found to be comparable to several commercially available ferrofluids. The obtained results further indicate that field induced heating efficiency increased by ~ 11 times on ~ 88% reduction in medium viscosity, which is due to the reduction in Brownian relaxation time of the dispersed magnetite nanoparticles at lower medium viscosity. Dynamic hysteresis loop simulations are carried out to theoretically estimate the heating efficiencies and the experimental and theoretical data are found to exhibit similar trends. The obtained results are beneficial for optimal design of bio-friendly oil based ferrofluids for possible topical hyperthermia applications over skin surfaces.

Heating Loss Mechanism in β-NaFeO <sub>2</sub> Nanoparticles for Cancer Treatment Under Alternating Field

The induction heating loss mechanism in nanofluids prepared using synthesized β-NaFeO2 nanoparticles have been discussed with respect to optimization of magnetic relaxation (Neel and Brownian) losses, specific absorption rate (SAR), intrinsic loss power (ILP)as well as concentration of nanoparticles. The highest value of SAR for β-NaFeO2 nanoparticles has been found to be 282.3 W/g at 335.2 Oe field and 267 kHz frequency.The value of Brownian and total relaxation time has been calculated theoretically and found to be τΒ= 6.126x10-4 sand τ= 2.668x10

Rotational dynamics of magnetic nanoparticles in different matrix systems

Abstract Dynamic magnetic measurements on magnetic nanoparticle (MNP) samples have been widely used for the determination of structural MNP parameters as well as for the realization of bioassays. On the other hand, proposed that the MNPs are thermally blocked, i.e., that the dynamics are dominated by the Brownian rotation, and knowing the distribution of their hydrodynamic size, information on the matrix properties can be obtained. In contrast to conventional rheology, the local environment of the MNPs is sensed on the nanoscale so that important information on the embedding of MNPs in the matrix and thus the particle-matrix interaction is obtained. Depending on the characteristic length scales of the matrix and the size of the MNPs, rheological parameters, such as viscosity and shear modulus, derived from nanorheological measurements can differ from the values obtained from conventional rheology. To measure the MNP dynamics, different experimental techniques can be applied. In this contribution, the focus lies on ac susceptometry and fluxgate magnetorelaxometry. The analysis of the complex ACS spectra is generally carried out within a modified Debye model. Different approaches for the estimation of rheological parameters from the complex ACS spectra will be presented. Two model systems will exemplarily be discussed in detail. As a Newtonian matrix system, water-glycerol mixtures were studied. It is demonstrated that the dynamic viscosity can accurately be estimated from ACS measurements on well thermally blocked single-core as well as on multicore MNP systems, which include Brownian and Néel dynamics. As a viscoelastic matrix system, aqueous gelatin solutions were studied. Gelatin is known to be a Voigt-Kelvin model system, in which elastic and viscous forces are parallel. In particular, we studied the gelation dynamics by repetitive measurements of the complex ACS spectrum. Different approaches to derive viscosity and shear modulus are applied and compared. In order to identify magnetoviscous effects in dynamic magnetic measurements, the magnetic field dependence of the Brownian relaxation time has to be eliminated. ACS measurements on various sufficiently strongly diluted aqueous MNP suspensions were performed in dependence of ac field amplitude and superimposed dc field strength and compared to theory. Excellent agreement was found.

Dependence of biomolecule detection on magnetic nanoparticle concentration

This paper investigates the influence of magnetic nanoparticle (MNP) concentration on biomolecule detection with magnetic particle spectroscopy (MPS). Streptavidin-coated MNPs, dominated by Brownian relaxation, are used to detect biotinylated Immunoglobulin G (IgG). The conjugation of the biotinylated IgG onto the surface of the functionalized MNPs enlarges their hydrodynamic sizes, thus increasing the Brownian relaxation time and changing the MPS signal. Experimental samples are prepared with Brownian relaxation-dominated MNP samples with different mole concentrations from 6.67 to 0.67 nM and IgG samples with different mole concentrations from 0 to 8.33 nM. Experimental results of ac susceptibility spectra indicate that the Brownian relaxation time increases from 0.85 to 1.20 ms with decreasing the MNP concentration from 6.67 to 0.67 nM at a given IgG concentration of 5 nM. Experimental results of MPS show that the ratio of the 3rd to 1st harmonics decreases more significantly with increasing IgG concentration at a lower MNP concentration. The absolute variation in the ratio of 3rd to 1st harmonics of the MNPs is used to characterize the measurement sensitivity of IgG. It shows that the measurement sensitivity increases from 1.68 × 10−3 to 12.25 × 10−3 nM−1 at an excitation frequency of 180 Hz. This study demonstrates that a lower MNP concentration can improve the measurement sensitivity of biomolecules with MPS in the frequency range from 180 to 1418 Hz. We emphasize that our findings are of great importance to reach a highly sensitive approach for biomolecule detection.

Magnetic nanoparticle-based biomolecule imaging with a scanning magnetic particle spectrometer

This study reports on a wash-free, inexpensive and sensitive approach of biomolecule imaging with magnetic nanoparticles (MNPs) via a custom-built scanning magnetic particle spectrometer (SMPS). Streptavidin-coated MNPs are used as magnetic biomarkers for the detection of Immunoglobulin G (IgG) conjugated with biotin (IgG-Biotin) while five samples with different-concentration IgG-Biotin are prepared for experiments. The measurements of the ac susceptibility indicate that the conjugation of the IgG-Biotin onto the surface of the MNPs forms cross-linking between the MNPs, thus increasing the characteristic Brownian relaxation time from 0.627 to 1.448 ms. The ratio of the 3rd to the 1st harmonics is measured on the samples with different-concentration IgG-Biotin in ac magnetic fields with a frequency ranging from about 300 Hz to 2 kHz. It shows that the measurement sensitivity of the IgG-Biotin concentration decreases from 4.62 × 10–3 to 0.39 × 10–3 nM−1 with increasing excitation frequency. Phantom images of the harmonic ratio, measured with the SMPS, indicate that unbound and bound MNPs can be easily distinguished. Furthermore, the excitation frequency dependence of the contrast-to-noise ratio of the images is discussed based on the measurement sensitivity and the standard deviation of the measured image intensity. This study demonstrates the feasibility of the SMPS for imaging biomolecules bound onto the MNPs, which is of great interest to disease diagnostics and therapy.

Wash-free detection of biological target using cluster formation of magnetic markers

We demonstrate the wash-free detection of biological targets based on the Brownian relaxation of magnetic markers. The Brownian relaxation time of bound markers was prolonged by using a cluster (or agglomerate) of bound markers that was formed via the binding reaction between markers and targets. Thus, bound and free markers were differentiated magnetically by using the difference in their relaxation times. Two types of magnetic properties, i.e., third-harmonic signal and magnetic relaxation, were used for measurement. The concentration of target was detected from the decrease in the third-harmonic signal and the increase in the magnetic-relaxation signal. We demonstrated the detection of C-reactive proteins using these two properties. In both cases, a good correlation was obtained between the measured signal and the concentration of target. It was also shown that the two methods had different concentration dependences, which will be caused mainly by the distribution of cluster size of the bound markers.

Magnetic field orientation dependent dynamic susceptibility and Brownian relaxation time of magnetic nanoparticles

This paper investigates the dynamic ac susceptibility (ACS) and the Brownian relaxation time of magnetic nanoparticles (MNPs) in dc magnetic fields with arbitrary orientations with respect to the ac magnetic field. A CoFe2O4 MNP sample, dominated by Brownian relaxation, is used to perform ACS measurements in an ac magnetic field with a constant amplitude of 0.2 mT (from 2 to 3000 Hz) and a superposed dc magnetic field with amplitudes ranging from 0 to 5 mT. Experimental results indicate that the ACS and Brownian relaxation time are significantly affected not only by the strength but also by the orientation of the dc magnetic field. Moreover, a mathematical model is proposed to analyze the ACS and Brownian relaxation time in dependence of the orientation of the dc magnetic field, which extends the established models parallel or perpendicular to arbitrary-oriented dc magnetic fields. Experimental results indicate that the good fitting between the experimental data (ACS and Brownian relaxation time) and the proposed models demonstrates the feasibility of the proposed model for the description of ACS and Brownian relaxation time in arbitrary-orientated ac and dc magnetic fields.

Numerical Model for Magnetic Fluid Hyperthermia in a Realistic Breast Phantom: Calorimetric Calibration and Treatment Planning.

This paper aims to apply a proposed, based on calorimetric measurements, a reliable numerical model for magnetic fluid hyperthermia (MFH) treatment planning of breast cancer. Furthermore, we perform a comparative analysis of magnetic nanoparticles (MNPs) and tumour tissue interactions by means of the magnetic-field-dependent Néel and Brownian relaxation times. The analysis was based on an anatomically correct breast model (developed in-house) and a modified linear response theory, which was applied to investigate the heat dissipation from the magnetic nanoparticles dispersed in the breast tumour. The calculations of the single-domain magnetic power losses were conducted for a case where the magnetic field value and the applied frequency were known, but also for the different concentrations of the MNPs in the tumour. Two scenarios were considered: The MNPs mobilised and immobilised in the tumour. In parallel, the eddy currents effect, together with the related temperature distributions, were considered in order to analyse safety issues. By changing the MNP concentration in the tumour, the corresponding temperature distributions were calculated. The eddy current effect, together with the related temperature distribution, were considered in order to analyse safety issues. Varying the MNP concentration in the tumour, the corresponding temperature distribution was calculated. Moreover, the cumulative equivalent minutes at were analysed. In the anatomically correct breast phantoms, the tissue location can lead to “hot spots” due to the eddy current effect and subsequently to the high gradients of the temperature. That is why the analysis of safety issues related to the overheating side effect should be taken into consideration during the treatment planning of magnetic fluid hyperthermia. The phenomenon of heat dissipation from MNPs is very sophisticated and depends on their concentration, the distribution and the relaxation mechanism in the tumour, together with magnetic field strength and frequency. Furthermore, we inferred that the phenomenon of heat dissipation from MNPs equally depends on MNP-tissue interactions, and it can lead to 30% differences in the power assessment. Nevertheless, the aforementioned factors should be considered in parallel using anatomical, volume-dependent models to enhance the efficiency of in vivo treatment.