Estimating the heating of complex nanoparticle aggregates for magnetic hyperthermia.

Understanding and predicting the heat released by magnetic nanoparticles is central to magnetic hyperthermia treatment planning. In most cases, nanoparticles form aggregates when injected in living tissues, thereby altering their response to the applied alternating magnetic field and preventing the accurate prediction of the released heat. We performed a computational analysis to investigate the heat released by nanoparticle aggregates featuring different sizes and fractal geometry factors. By digitally mirroring aggregates seen in biological tissues, we found that the average heat released per particle stabilizes starting from moderately small aggregates, thereby facilitating making estimates for their larger counterparts. Additionally, we studied the heating performance of particle aggregates over a wide range of fractal parameters. We compared this result with the heat released by non-interacting nanoparticles to quantify the reduction of heating power after being instilled into tissues. This set of results can be used to estimate the expected heating in vivo based on the experimentally determined nanoparticle properties.

Monitoring magnetic nanoparticle clustering and immobilization with thermal noise magnetometry using optically pumped magnetometers.

Thermal noise magnetometry (TNM) is a recently developed magnetic characterization technique where thermally induced fluctuations in magnetization are measured to gain insight into nanomagnetic structures like magnetic nanoparticles (MNPs). Due to the stochastic nature of the method, its signal amplitude scales with the square of the volume of the individual fluctuators, which makes the method therefore extra attractive to study MNP clustering and aggregation processes. Until now, TNM signals have exclusively been detected by using a superconducting quantum interference device (SQUID) sensor. In contrast, we present here a tabletop setup using optically pumped magnetometers (OPMs) in a compact magnetic shield, as a flexible alternative. The agreement between results obtained with both measurement systems is shown for different commercially available MNP samples. We argue that the OPM setup with low complexity complements the SQUID setup with high sensitivity and bandwidth. Furthermore, the OPM tabletop setup is well suited to monitor aggregation processes because of its excellent sensitivity in lower frequencies. As a proof of concept, we show the changes in the noise spectrum for three different MNP immobilization and clustering processes. From our results, we conclude that the tabletop setup offers a flexible and widely adoptable measurement unit to monitor the immobilization, aggregation, and clustering of MNPs for different applications, including interactions of the particles with biological systems and the long-term stability of magnetic samples.

Individual particle heating of interacting magnetic nanoparticles at nonzero temperature.

Interaction phenomena have become a hot topic in nanotechnology due to their influence on the performance of magnetic nanostructures for biomedical applications. Hysteresis loops give a good account of the particles' magnetic behaviour, providing valuable clues on subsequent improvements. Nevertheless, the individual hysteresis loops of these systems are also influenced by any potential energy exchanged between the particles, and in contrast to non-interacting particles, are no longer a good measure for the local heat generated by each particle. As of today, there is no method capable of analysing the heat dissipation resulting from the nanoscale magnetisation dynamics in its full generality, i.e. in the presence of interactions and at nonzero temperature (allowing for thermally induced switching), and therefore the means of exploiting these dynamics remain hampered by a lack of understanding. In this work we address this problem by proposing and validating an equation that can be used to resolve the individual heat dissipation of interacting nanoparticles at nonzero temperature. After assessing this equation for different model systems, we have found that the proportion of heat dissipated in each individual particle tends to become more uniformly distributed for larger fields. Our results might have implications for magnetic particle hyperthermia where one of the most long-standing challenges is to achieve a homogeneous therapeutic temperature distribution in the target region during a treatment. Although tackling this issue involves a number of aspects related to the tissues involved, the injected nanoparticles, and the applied magnetic field, we believe that a more homogeneous heating of the particles inside the tumour will help to overcome this challenge.

Advanced analysis of magnetic nanoflower measurements to leverage their use in biomedicine.

Magnetic nanoparticles are an important asset in many biomedical applications ranging from the local heating of tumours to targeted drug delivery towards diseased sites. Recently, magnetic nanoflowers showed a remarkable heating performance in hyperthermia experiments thanks to their complex structure leading to a broad range of magnetic dynamics. To grasp their full potential and to better understand the origin of this unexpected heating performance, we propose the use of Kaczmarz' algorithm in interpreting magnetic characterisation measurements. It has the advantage that no a priori assumptions need to be made on the particle size distribution, contrasting current magnetic interpretation methods that often assume a lognormal size distribution. Both approaches are compared on DC magnetometry, magnetorelaxometry and AC susceptibility characterisation measurements of the nanoflowers. We report that the lognormal distribution parameters vary significantly between data sets, whereas Kaczmarz' approach achieves a consistent and accurate characterisation for all measurement sets. Additionally, we introduce a methodology to use Kaczmarz' approach on distinct measurement data sets simultaneously. It has the advantage that the strengths of the individual characterisation techniques are combined and their weaknesses reduced, further improving characterisation accuracy. Our findings are important for biomedical applications as Kaczmarz' algorithm allows to pinpoint multiple, smaller peaks in the nanostructure's size distribution compared to the monomodal lognormal distribution. The smaller peaks permit to fine-tune biomedical applications with respect to these peaks to e.g. boost heating or to reduce blurring effects in images. Furthermore, the Kaczmarz algorithm allows for a standardised data analysis for a broad range of magnetic nanoparticle samples. Thus, our approach can improve the safety and efficiency of biomedical applications of magnetic nanoparticles, paving the way towards their clinical use.

Finite difference magnetoelastic simulator.

We describe an extension of the micromagnetic finite difference simulation software MuMax3 to solve elasto-magneto-dynamical problems. The new module allows for numerical simulations of magnetization and displacement dynamics in magnetostrictive materials and structures, including both direct and inverse magnetostriction. The theoretical background is introduced, and the implementation of the extension is discussed. The magnetoelastic extension of MuMax3 is freely available under the GNU General Public License v3.

Simultaneous Coercivity and Size Determination of Magnetic Nanoparticles.

Magnetic nanoparticles are increasingly employed in biomedical applications such as disease detection and tumor treatment. To ensure a safe and efficient operation of these applications, a noninvasive and accurate characterization of the particles is required. In this work, a magnetic characterization technique is presented in which the particles are excited by specific pulsed time-varying magnetic fields. This way, we can selectively excite nanoparticles of a given size so that the resulting measurement gives direct information on the size distribution without the need for any a priori assumptions or complex postprocessing procedures to decompose the measurement signal. This contrasts state-of-the-art magnetic characterization techniques. The possibility to selectively excite certain particle types opens up perspectives in "multicolor" particle imaging, where different particle types need to be imaged independently within one sample. Moreover, the presented methodology allows one to simultaneously determine the size-dependent coercivity of the particles. This is not only a valuable structure-property relation from a fundamental point of view, it is also practically relevant to optimize applications like magnetic particle hyperthermia. We numerically demonstrate that the novel characterization technique can accurately reconstruct several particle size distributions and is able to retrieve the coercivity-size relation of the particles. The developed technique advances current magnetic nanoparticle characterization possibilities and opens up exciting pathways for biomedical applications and particle imaging procedures.

Design of Intense Nanoscale Stray Fields and Gradients at Magnetic Nanorod Interfaces.

We explore electrodeposited ordered arrays of Fe, Ni, and Co nanorods embedded in anodic alumina membranes as a source of intense magnetic stray field gradients localized at the nanoscale. We perform a multiscale characterization of the stray fields using a combination of experimental methods (magnetooptical Kerr effect and virtual bright field differential phase contrast imaging) and micromagnetic simulations and establish a clear correlation between the stray fields and the magnetic configurations of the nanorods. For uniformly magnetized Fe and Ni wires, the field gradients vary following saturation magnetization of the corresponding metal and the diameter of the wires. In the case of Co nanorods, very localized (∼10 nm) and intense (>1 T) stray field sources are associated with the cores of magnetic vortexes. Confinement of that strong field at extremely small dimensions leads to exceptionally high field gradients up to 108 T/m. These results demonstrate a clear path to design and fine-tune nanoscale magnetic stray field ordered patterns with a broad applicability in key nanotechnologies, such as nanomedicine, nanobiology, nanoplasmonics, and sensors.

Dynamical Magnetic Response of Iron Oxide Nanoparticles Inside Live Cells.

Magnetic nanoparticles exposed to alternating magnetic fields have shown a great potential acting as magnetic hyperthermia mediators for cancer treatment. However, a dramatic and unexplained reduction of the nanoparticle magnetic heating efficiency has been evidenced when nanoparticles are located inside cells or tissues. Recent studies suggest the enhancement of nanoparticle clustering and/or immobilization after interaction with cells as possible causes, although a quantitative description of the influence of biological matrices on the magnetic response of magnetic nanoparticles under AC magnetic fields is still lacking. Here, we studied the effect of cell internalization on the dynamical magnetic response of iron oxide nanoparticles (IONPs). AC magnetometry and magnetic susceptibility measurements of two magnetic core sizes (11 and 21 nm) underscored differences in the dynamical magnetic response following cell uptake with effects more pronounced for larger sizes. Two methodologies have been employed for experimentally determining the magnetic heat losses of magnetic nanoparticles inside live cells without risking their viability as well as the suitability of magnetic nanostructures for in vitro hyperthermia studies. Our experimental results-supported by theoretical calculations-reveal that the enhancement of intracellular IONP clustering mainly drives the cell internalization effects rather than intracellular IONP immobilization. Understanding the effects related to the nanoparticle transit into live cells on their magnetic response will allow the design of nanostructures containing magnetic nanoparticles whose dynamical magnetic response will remain invariable in any biological environments, allowing sustained and predictable in vivo heating efficiency.

Creep turns linear in narrow ferromagnetic nanostrips.

The motion of domain walls in magnetic materials is a typical example of a creep process, usually characterised by a stretched exponential velocity-force relation. By performing large-scale micromagnetic simulations, and analyzing an extended 1D model which takes the effects of finite temperatures and material defects into account, we show that this creep scaling law breaks down in sufficiently narrow ferromagnetic strips. Our analysis of current-driven transverse domain wall motion in disordered Permalloy nanostrips reveals instead a creep regime with a linear dependence of the domain wall velocity on the applied field or current density. This originates from the essentially point-like nature of domain walls moving in narrow, line- like disordered nanostrips. An analogous linear relation is found also by analyzing existing experimental data on field-driven domain wall motion in perpendicularly magnetised media.

Quantitative model selection for enhanced magnetic nanoparticle imaging in magnetorelaxometry.

PURPOSE: The performance of an increasing number of biomedical applications is dependent on the accurate knowledge of the spatial magnetic nanoparticle (MNP) distribution in the body. Magnetorelaxometry (MRX) imaging is a promising and noninvasive technique for the reconstruction of this distribution. To date, no accurate and quantitative measure is available to compare and optimize different MRX imaging models and setups independent of the MNP distribution. In this paper, the authors employ statistical parameters to develop quantitative MRX imaging models. Using these models, a straightforward optimization of setups and models is possible resulting in improved MNP reconstructions. METHODS: A MRX imaging setup is considered with different coil configurations, each corresponding to a MRX imaging model. The models can be represented by a sensitivity matrix. These are compared by employing the matrices as inputs to statistical parameters such as conditional entropy and mutual information (MI). These parameters determine the best model to reconstruct the MNP amount for each volume-element (voxel) in the sample. The matrix is transformed by multiplying the columns with different weightings depending on the performance of the MRX imaging model with respect to the other models. This transformed matrix is compared to the original sensitivity matrix without weightings. RESULTS: Compared to the original sensitivity matrix, an increased numerical stability and improved noise robustness for the transformed sensitivity matrix are observed. The reconstruction of the MNP shows improvements: a correlation to the actual MNP distribution of 99.2%, whereas the original matrix only had 82.5%. By selecting the MRX models with the smallest MI, the authors are able to reduce the measurement time by 65% and still obtain an improved imaging accuracy and noise robustness. The statistical parameters allow a direct measure of the relative information content within the setup such that the optimal voxel size for the MRX setup is determined to be between 5 and 15 mm, while other sizes show a significant change in the statistical parameters. CONCLUSIONS: The use of statistical parameters in MRX imaging models results in quantitative models which can optimize MRX setups in a very fast and elegant way such that improved MNP imaging can be realized. Finally, the presented measure allows to quantitatively and accurately compare different MRX models and setups independent of the MNP distribution.

Vinamax: a macrospin simulation tool for magnetic nanoparticles.

We present Vinamax, a simulation tool for nanoparticles that aims at simulating magnetization dynamics on very large timescales. To this end, each individual nanoparticle is approximated by a macrospin. Vinamax numerically solves the Landau-Lifshitz equation by adopting a dipole approximation method, while temperature effects can be taken into account with two stochastic methods. It describes the influence of demagnetizing and anisotropy fields on magnetic nanoparticles at finite temperatures in a space- and time-dependent externally applied field. Vinamax can be used in biomedical research where nanoparticle imaging techniques are under development, e.g., to validate other higher-level models and study their limitations.