| Zusammenfassung |
Magnetic nanoparticles (MNPs) are widely used in biomedical applications. With typical diameters of several tens to a few hundred nanometers, they are ideally suited to approach or enter biological entities. Additionally, their surfaces can be functionalized to target specific biological systems. Their magnetic properties allow us to manipulate them with external magnetic fields so that they can be steered, imaged, and heated inside the human body. Today, MNPs are used as contrast agents in magnetic resonance imaging and for cancer therapy in MNP-based hyperthermia. Several other biomedical applications that make use of MNPs, such as targeted drug delivery and magnetic particle imaging, are in different stages of development.
The prerequisite for the safe, efficient, and reliable usage of MNPs is a detailed characterization of their properties. An important part of this characterization is the determination of the static and dynamical magnetic properties since these define their magnetic behavior under the fields applied in the applications. Additionally, the physical properties of the MNPs, such as e.g. the size distribution of the ensemble, influence the dynamical properties of their magnetic moments. In all of the magnetic characterization techniques, one determines the magnetization dynamics by recording the response of the MNPs to an external excitation. These techniques probe different aspects of the magnetization under different conditions. This way, a complete picture of the magnetic properties is obtained. However, the various arrangements also make it hard to consistently compare results. Moreover, the external field that is used for the excitation potentially induces changes in the state of the particles, they can e.g. aggregate or form chains along the magnetic field lines. In this case, the measurement procedure influences the results.
But what if one doesn’t have to stimulate the MNPs at all? Due to thermal energy, the magnetic moments constantly reorient themselves, thereby creating tiny fluctuations on the magnetic signal of an MNP ensemble. These intrinsic fluctuations in the magnetization are inherently related to the particles’ properties, and can thus be used as a measurement input for MNP characterization purposes. The measurement and analysis of these thermal fluctuations in MNP systems is called Thermal Noise Magnetometry (TNM). TNM has the advantage that the particles are in a strict thermal equilibrium during the measurement and that there is no need for an external excitation that can possibly bias the result. The feasibility of these type of measurements was proven in earlier work, and the similarity and complementarity with other characterization techniques verified. However, there are several remaining questions regarding TNM, both of scientific and practical nature. This thesis aims to further develop the theory of TNM, propel its experimental realization, and establish it as an MNP characterization technique.
Chapter 1 contains an extensive introduction to MNPs. We present some of their biomedical applications and discuss their magnetic properties under a static and time-variant field. We give a few examples of thermal noise in physical systems, introduce TNM as an MNP characterization technique, and describe the outline of the thesis. In Chapter 2 we present the methods that were used and developed in the light of this work to study the thermal fluctuations in MNP ensembles. They are a combination of modeling, measuring, and simulating. Since thermal noise is stochastic, a summary of the most important aspects of probability theory is given. We use the stochastic framework and apply it to the specific case of MNP ensembles. This allows us to define a fluctuation amplitude and characteristic timescale for the two fluctuation mechanisms: the Brownian mechanism, where particles physically rotate in a suspension, and the Néel mechanism, where the magnetic moments rotate with respect to the crystal structure itself. Then, the experimental setup and its digital twin in the macrospin simulation tool Vinamax are introduced, which can be used complementary. Finally, a practical guide for the calculation of the Power Spectral Density (PSD), the characteristic curve in TNM, from a discrete signal is given.
In Chapter 3, the TNM signal strength is studied. The signal is stochastic in nature, inherently small, and difficult to measure - even with the most sensitive magnetometers. The TNM signal strength can be calculated as the variance of the stochastic variable, or as the integration of the PSD over the full frequency range. It is shown that both methods yield comparable values for a polydisperse MNP ensemble, which allows to compare experimental and numerical results. The scaling of the signal amplitude with the number of particles and their volume is determined, both for a variable and fixed total iron amount in the sample. An interesting result is the intrinsic high sensitivity of TNM to MNP cluster events, a property which will be exploited in chapter 5. To address the small signal strength, the geometry of the experiment is optimized in favor of the TNM signal by calculating an optimal sampleholder shape. The holder is constructed and used for experiments, increasing the signal with a factor of 3.5 with less than half of the magnetic material required.
Chapter 4 focuses on the impact of temperature on the thermal fluctuations, a central parameter whose influence on the PSD was not well understood yet. The presented model of Chapter 2 is compared with simulations of the thermal fluctuations in a single MNP at different temperatures. The fluctuation amplitude is independent of temperature for the Brownian mechanism, and the timescales vary only slightly. However, for Néel fluctuations, the fluctuation amplitude does depend on temperature, and the timescales vary strongly. Then, the theory is extended to a polydisperse sample, which is studied at different biomedically relevant temperatures with experiments and simulations. A high change in noise power for lower frequency is found, which potentially can be used as a local temperature probe.
In Chapter 5, we present a TNM tabletop system that was developed to make TNM experiments more flexible by replacing the sofar used SQUID sensor with an alternative sensor system based on Optically Pumped Magnetometers (OPMs). By a proper gain calibration of the OPMs, we are able to extend the bandwidth of the sensors to 500 Hz. TNM measurements of two MNP systems in the OPM-based setup were confirmed by SQUID-based measurements. Driven by the flexibility of the tabletop setup, the sensitivity of TNM to clustering events, and the good performance of the OPMs in the lower frequency range - which covers typical changes in the MNPs fluctuations induced by the biological environment - we investigate the employability of the tabletop setup for the monitoring of changes in the fluctuation dynamics of MNPs’ state. Three proof-of-principle experiments are performed to prove the suitability of the tabletop setup to investigate the effect of MNP clustering, immobilization, and aggregation on the TNM signal.
In Chapter 6 the main results of this thesis are summarized and we provide the future prospects of TNM as a characterization technique of MNPs. |
