Quantitative reconstruction of a magnetic nanoparticle distribution using a non-negativity constraint

Magnetorelaxometry (MRX) is a non-invasive method for the specific quantification of magnetic nanoparticles (MNP). Here, we investigate experimentally the reconstruction of the MNP concentration in an extended volume. A phantom with varying but known MNP distribution was subsequently magnetized by 48 planar coils at different locations. The MRX signal was measured using the PTB 304 SQUID-magnetometer system. The inverse problem was solved by means of a non-negative least squares (NNLS) algorithm and compared to a minimum norm estimation (TSVD-MNE). The reconstruction by NNLS shows a deviation of the total MNP amount of less than 3 % (10% by TSVD-MNE). Hence, adapted non-invasive MRX methods can reliable reconstruct the MNP content in extended volumes

Improving Condition and Sensitivity of Linear Inverse Problems in Magnetic Applications

Die Identifikation nicht direkt zugänglicher Prozesse anhand gemessener Daten ist von großer Bedeutung in vielen Bereichen. Im Fokus dieser Arbeit liegen Applikationen in der Magnetostatik, Magnetokardiographie und Magnetinduktionstomographie. Ein Ansatz zur Identifikation besteht in der Lösung eines entsprechenden linear inversen Problems. Unglücklicherweise haben in den Daten enthaltene Fehler und Rauschen einen signifikanten Einfluss auf die inverse Lösung. Ziel dieser Arbeit ist die Reduktion der Einflüsse von Fehlern und Rauschen durch eine Verbesserung der Kondition des Problems, sowie eine Steigerung der Sensitivität der Messanordnungen. Zur Bestimmung der Kondition wird das Verhältnis des größten und mittleren Singulärwerts der Kernmatrix als neues Maß vorgeschlagen. Darüber hinaus werden Ansätze zur Analyse der Sensitivität hinsichtlich der Messung elektromagnetischer Quellen und der Erfassung elektrischer Leitfähigkeitsveränderungen präsentiert.Strategien zur Verbesserung von Kondition und Sensitivität werden in vier Simulationsstudien beschrieben. In der ersten Studie wird ein Tabu-Suche-Ansatz zur Optimierung der Anordnung magnetischer Sensoren vorgestellt. Anordnungen mit optimierte Sensorpositionen resultieren dabei in einer deutlich besseren Kondition als regelmäßige Anordnungen. In einer zweiten Studie werden Parameter adaptiert,welche den Quellenraum für die Bildgebung durch magnetische Nanopartikel definieren. Als eine Schlussfolgerung sollte der Quellenraum etwas größer als das Sensorareal definiert werden. Diese Arbeit zeigt ebenfalls, dass Variationen in den Sensorrichtungen für monoaxiale Sensorarrays zu einer Verbesserung der Kondition führen. Zudem wird die Sensitivität von Spulenanordnungen für die Magnetinduktionstomographie bewertet und verglichen. Durch Nutzung relativ großer Spulen, die das Messgebiet nahezu vollständig abdecken, können Kondition und Sensitivität wesentlich verbessert werden.Die präsentierten Methoden und Strategien ermöglichen eine substantielle Verbesserung der Kondition des linear inversen Problems bei der Analyse magnetischer Messungen. Insbesondere die Anordnung von Sensoren in Bezug auf das Messobjekt ist kritisch für die Kondition, sowie die Qualität inverser Lösungen. Die vorgestellten Methoden sind darüber hinaus für linear inverse Probleme in zahlreichen Bereichen einsetzbar.The identification and reconstruction of hidden, not directly accessible processes from measured data is important in many areas of research and engineering. This thesis focusses on applications in magnetostatics, magnetocardiography, and magneticinduction tomography. One approach to identify these processes is to solve a related linear inverse problem. Unfortunately, noise and errors in the data have a significant impact on inverse solutions.The aim of this work is to reduce the effects of noise and errors by improving the condition of the problem and to increase the sensitivity of measurement setups. To quantify the condition, we propose the ratio of the largest and the mean singular value of the kernel matrix. Moreover, we outline approaches to analyse quantitatively and qualitatively the sensitivity to electromagnetic sources and electrical conductivity changes.In four simulation studies, strategies to improve the condition and sensitivity inmagnetic applications are described. First, we present a tabu search algorithm to optimize arrangements of magnetic sensors. Optimized sensor arrays result in a considerably improved condition compared with regular arrangements. Second, we adapt parameters that define source space grids for magnetic nanoparticle imaging. One conclusion is that the source space should be defined slightly larger than the sensor area. Third, we demonstrate for mono-axial sensor arrays that variations in thesensor directions and small variations in the sensor positions lead to improvements of the condition, too. Finally, we evaluate and compare the sensitivities of six coil setups for magnetic induction tomography. Our investigations indicate a rapid decay of sensitivity by several orders of magnitude within a range of a few centimetres. By using relatively large coils that cover the measurement region almost completely, the condition and sensitivity can be improved clearly.The methods and strategies presented in this thesis facilitate substantial improvements of the condition for linear inverse problems in magnetic applications. In particular, the arrangement of sensors relative to the measurement object is critical to the condition and to the quality of inverse solutions. Moreover, the presented methods are applicable to linear inverse problems in various fields

Magnetic measurement methods to probe nanoparticle–matrix interactions

Magnetic nanoparticles (MNPs) are key elements in several biomedical applications, e.g., in cancer therapy. Here, the MNPs are remotely manipulated by magnetic fields from outside the body to deliver drugs or generate heat in tumor tissue. The efficiency and success of these approaches strongly depend on the spatial distribution and quantity of MNPs inside a body and interactions of the particles with the biological matrix. These include dynamic processes of the MNPs in the organism such as binding kinetics, cellular uptake, passage through cell barriers, heat induction and flow. While magnetic measurement methods have been applied so far to resolve the location and quantity of MNPs for therapy monitoring, these methods can be advanced to additionally access these particle–matrix interactions. By this, the MNPs can further be utilized as probes for the physical properties of their molecular environment. In this review, we first investigate the impact of nanoparticle–matrix interactions on magnetic measurements in selected experiments. With these results, we then advanced the imaging modalities magnetorelaxometry imaging and magnetic microsphere tracking to spatially resolve particle–matrix interactions

Forward and inverse calculation methods for Lorentz force evaluation applied to laminated composites

The classification of material deficiencies is a key feature in quality assurance. In this framework, laminated composite materials are of special interest, because they increasingly replace monolithic materials. The Lorentz force evaluation (LFE) is an evaluation technique to reconstruct the geometry of flaws in electrically conducting composites using inverse calculations. These calculations are based on perturbations that occur in the measured Lorentz force signals and are caused by the flaws. The force signals are obtained using the nondestructive testing method Lorentz force eddy current testing (LET). In this electromagnetic technique, a permanent magnet and the material under investigation move relative to each other. As a consequence eddy currents are induced in the conductor. The eddy currents in turn interact with the magnetic field and cause a Lorentz force. Inverse calculations in LFE require a forward solution of the measured force signals, which incorporates a model of the LET setup. The objective of this thesis is the development and evaluation of forward and inverse calculation methods for LFE. The proposed methods are assessed using Lorentz force data obtained from laminated composites. In order to model the permanent magnet in the forward solution for LFE the magnetic dipoles model (MDM) is introduced. In the MDM, a permanent magnet is represented by an assembly of magnetic dipoles. An optimization procedure is used to determine optimal dipole positions. Contrary to analytic models the MDM can be applied to permanent magnets of arbitrary geometry, and forward calculations can be performed with analytic mathematics. For defect reconstruction three inverse methods are introduced in this thesis. In the first method, conductivity reconstructions are performed using a stochastic optimization algorithm, the Differential Evolution (DE). Prior to inverse calculations, the intrinsic control parameters of the DE are determined based on parameter studies. As the second inverse strategy, current density reconstructions (CDR) calculated with minimum norm estimates (MNE) are employed. This approach is based on interpreting a defect in the forward solution for LFE as a distributed current source. In the third method, a goal function scan is performed to reconstruct the geometry parameters of the defect. All three inverse methods are suitable for reconstructing defects, whereas the first and third method provide more accurate results than the second. Further, measured Lorentz force signals obtained from glass laminate aluminum reinforced epoxy (GLARE) composite are investigated. GLARE is widely used in the aircraft industry. The flaw detectability of LET and LFE for GLARE is proved.Die Klassifizierung von Materialdefekten ist ein wesentliches Merkmal der Qualitätssicherung. Dabei sind geschichtete Verbundwerkstoffe von besonderem Interesse, weil sie zunehmend monolithische Werkstoffe ersetzen. Lorentz force evaluation (LFE) ist eine Methode zur Rekonstruktion der Geometrie von Fehlstellen in elektrisch leitfähigen Verbundwerkstoffen mittels inverser Berechnungen. Die Grundlage der inversen Berechnungen sind Störungen, die aufgrund der Fehlstellen in den gemessenen Lorentzkraft-Signalen auftreten. Die Signale werden mittels der zerstörungsfreien Prüfmethode, der Lorentzkraft-Wirbelstromprüfung (LET) gemessen. Bei diesem elektromagnetischen Testverfahren bewegen sich ein Permanentmagnet und das zu untersuchende Material relativ zu einander. Dadurch werden Wirbelströme im Material induziert. Die Interaktion dieser mit dem Magnetfeld hat eine Lorentzkraft zur Folge. Für inverse Verfahren ist eine Vorwärtslösung zur Berechnung der Lorentzkraft notwendig, der ein Modell des LET-Aufbaus zugrunde liegt. Das Ziel der vorliegenden Dissertation ist die Entwicklung und Evaluierung von Vor-wärtslösungen und inversen Berechnungsmethoden für LFE. Zur Bewertung der Methoden werden Lorentzkraft Signale verwendet, die aus Messungen von geschichteten Verbundmaterialien stammen. Zur Modellierung des Permanentmagneten in der Vorwärtslösung für LFE wird das Magnetische-Dipole-Modell (MDM) entwickelt. In diesem Modell wird ein Permanentmagnet durch eine Verteilung magnetischer Dipole repräsentiert. Die Positionen der magnetischen Dipole werden optimiert. Im Vergleich zu analytischen Modellen kann das MDM zur Modellierung beliebig geformter Permanentmagneten verwendet werden. Die Lorentzkraft-Signale können analytisch berechnet werden. In dieser Dissertation werden drei inverse Berechnungsmethoden für LFE erarbeitet. In der ersten Methode wird ein stochastischer Optimierungsalgorithmus, der Differential Evolution, zur Rekonstruktion von Leitfähigkeiten im Material verwendet. Die intrinsischen Kontrollparameter des Differential Evolution (DE) werden anhand von Parameterstudien festgelegt. Als zweite inverse Methode werden Stromdichterekonstruktionen mittels Minimum-Norm-Schätzungen durchgeführt. Grundlegend für diesen Ansatz ist die Interpretation eines Defektes in der Vorwärtslösung als verteilte Stromquelle. Als dritte inverse Methode wird eine Abtastung der Zielfunktion zur Rekonstruktion der Defektparameter vorgenommen. Alle inversen Verfahren sind zur Defektrekonstruktion geeignet, wobei sich die Ergebnisse der ersten und dritten Methode genauer darstellen als die der zweiten. Des Weiteren werden Messdaten eines aus glasfaserverstärktem Aluminium (GLARE) bestehenden Prüfkörpers ausgewertet. GLARE wird insbesondere im Flugzeugbau eingesetzt. Es wird gezeigt, dass mit LET und LFE Materialfehler in GLARE nachgewiesen werden können

Characterisation and State Estimation of Magnetic Soft Continuum Robots

Minimally invasive surgery has become more popular as it leads to less bleeding, scarring, pain, and shorter recovery time. However, this has come with counter-intuitive devices and steep surgeon learning curves. Magnetically actuated Soft Continuum Robots (SCR) have the potential to replace these devices, providing high dexterity together with the ability to conform to complex environments and safe human interactions without the cognitive burden for the clinician. Despite considerable progress in the past decade in their development, several challenges still plague SCR hindering their full realisation. This thesis aims at improving magnetically actuated SCR by addressing some of these challenges, such as material characterisation and modelling, and sensing feedback and localisation. Material characterisation for SCR is essential for understanding their behaviour and designing effective modelling and simulation strategies. In this work, the material properties of commonly employed materials in magnetically actuated SCR, such as elastic modulus, hyper-elastic model parameters, and magnetic moment were determined. Additionally, the effect these parameters have on modelling and simulating these devices was investigated. Due to the nature of magnetic actuation, localisation is of utmost importance to ensure accurate control and delivery of functionality. As such, two localisation strategies for magnetically actuated SCR were developed, one capable of estimating the full 6 degrees of freedom (DOFs) pose without any prior pose information, and another capable of accurately tracking the full 6-DOFs in real-time with positional errors lower than 4~mm. These will contribute to the development of autonomous navigation and closed-loop control of magnetically actuated SCR

A numerical investigation of hydrocarbon related magnetic signatures

The iron sulphide greigite (Fe3S4) is linked to important diagenetic processes in sediments and to hydrocarbon formation and migration. The magnetic properties of this ferrimagnetic mineral are relatively obscure because it is difficult to synthesise and because it is unstable and therefore thought to be irrelevant to the geological record. However, it is increasingly recognised that greigite can remain stable on geological timescales. It is important to understand the magnetic properties of greigite to identify its presence and timing of formation as it is a proxy for environmental magnetic studies and for hydrocarbon microseepage identification. In this thesis, numerical methods are used to study the magnetic properties of greigite. Using a micromagnetic finite-element method (FEM), important questions regarding the magnetic structure and palaeomagnetic recording fidelity of gregite are addressed. For equidimensional particles, the single-domain (SD) to single-vortex (SV) threshold is found to be $d_0\approx 54$ nm and only SV particles >70 nm to carry stable magnetisations over billion-year timescales. A simplified model is developed to study the hysteresis and first-order reversal curve (FORC) properties of non-interacting idealised SD greigite particles. To understand the effects of SV magnetisations on FORC properties, a micromagnetic FEM is used to simulate randomly oriented dispersions of non-interacting greigite in the SV size range. SV effects dominate the FORC signal for particles >70 nm. Implications for FORC diagram interpretation are discussed. Magnetic inter-particle interactions are known to effect the FORC response of magnetic particle ensembles. A micromagnetic FEM is used to study the FORC signal of randomly dispersed strongly interacting clusters of greigite. The FORC response of strongly interacting greigite is found to be similar to that of multi-domain (MD) particles. Since naturally occurring greigite is rarely in a MD state, it is concluded that in greigite-bearing rocks that produce MD-like FORC signals the origin of this signal should be attributed to strong interactions between the particles.Open Acces