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Modeling the Magnetization Dynamics for Large Ensembles of Immobilized Magnetic Nanoparticles in Multi-dimensional Magnetic Particle Imaging
TL;DR: In this article, a model-based approach for magnetic particle imaging (MPI) has been proposed, where the magnetization response is simulated by a Neel rotation model for the particle's magnetic moments and the ensemble magnetization is obtained by solving a Fokker-Planck equation approach.
Abstract: Magnetic nanoparticles (MNPs) play an important role in biomedical applications including imaging modalities such as MRI and magnetic particle imaging (MPI). The latter one exploits the non-linear magnetization response of a large ensemble of magnetic nanoparticles to magnetic fields which allows determining the spatial distribution of the MNP concentration from measured voltage signals. Currently, modeling the voltage signals of large ensembles of MNPs in an MPI environment is not yet accurately possible, especially for liquid tracers in multi-dimensional magnetic excitation fields. Thus, the voltage-to-image mapping is still obtained in a time consuming calibration procedure. While the ferrofluidic case can be seen as the typical setting, more recently immobilized and potentially oriented MNPs have received considerable attention. By aligning the particles during immobilization, one can encode the angle of the easy axis into the magnetization response providing a sophisticated benchmark system for model-based approaches. In this work, we address the modeling problem for immobilized, oriented MNPs in the context of MPI. We investigate a model-based approach where the magnetization response is simulated by a Neel rotation model for the particle's magnetic moments and the ensemble magnetization is obtained by solving a Fokker-Planck equation approach. Since the parameters of the model are a-priori unknown, we investigate different methods for performing a parameter identification and discuss two models: One where a single function vector is used from the space spanned by the model parameters and another where a superposition of function vectors is considered. We show that our model can much more accurately reproduce the orientation dependent signal response when compared to the equilibrium model, which marks the current state-of-the-art for model-based system matrix simulations in MPI.
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01 Jun 1972
TL;DR: In this paper, the authors present materials at the practical rather than theoretical level, allowing for a physical, quantitative, measurement-based understanding of magnetism among readers, be they professional engineers or graduate-level students.
Abstract: Introduction to Magnetic Materials, 2nd Edition covers the basics of magnetic quantities, magnetic devices, and materials used in practice. While retaining much of the original, this revision now covers SQUID and alternating gradient magnetometers, magnetic force microscope, Kerr effect, amorphous alloys, rare-earth magnets, SI Units alongside cgs units, and other up-to-date topics. In addition, the authors have added an entirely new chapter on information materials. The text presents materials at the practical rather than theoretical level, allowing for a physical, quantitative, measurement-based understanding of magnetism among readers, be they professional engineers or graduate-level students.
6,573 citations
TL;DR: This paper discusses targeted drug delivery and triggered release, novel contrast agents for magnetic resonance imaging, cancer therapy using magnetic fluid hyperthermia, in vitro diagnostics and the emerging magnetic particle imaging technique that is quantitative and sensitive enough to compete with established imaging methods.
Abstract: Biomedical nanomagnetics is a multidisciplinary area of research in science, engineering and medicine with broad applications in imaging, diagnostics and therapy. Recent developments offer exciting possibilities in personalized medicine provided a truly integrated approach, combining chemistry, materials science, physics, engineering, biology and medicine, is implemented. Emphasizing this perspective, here we address important issues for the rapid development of the field, i.e., magnetic behavior at the nanoscale with emphasis on the relaxation dynamics, synthesis and surface functionalization of nanoparticles and core-shell structures, biocompatibility and toxicity studies, biological constraints and opportunities, and in vivo and in vitro applications. Specifically, we discuss targeted drug delivery and triggered release, novel contrast agents for magnetic resonance imaging, cancer therapy using magnetic fluid hyperthermia, in vitro diagnostics and the emerging magnetic particle imaging technique, that is quantitative and sensitive enough to compete with established imaging methods. In addition, the physics of self-assembly, which is fundamental to both biology and the future development of nanoscience, is illustrated with magnetic nanoparticles. It is shown that various competing energies associated with self-assembly converge on the nanometer length scale and different assemblies can be tailored by varying particle size and size distribution. Throughout this paper, while we discuss our recent research in the broad context of the multidisciplinary literature, we hope to bridge the gap between related work in physics/chemistry/engineering and biology/medicine and, at the same time, present the essential concepts in the individual disciplines. This approach is essential as biomedical nanomagnetics moves into the next phase of innovative translational research with emphasis on development of quantitative in vivo imaging, targeted and triggered drug release, and image guided therapy including validation of delivery and therapy response.
717 citations
TL;DR: The quality of the least-squares solution can be improved by incorporating a weighting matrix using the reciprocal of the matrix-row energy as weights and this weighting strategy in combination with the conjugate gradient method improves the image quality and substantially shortens the reconstruction time.
Abstract: Magnetic particle imaging (MPI) is a new imaging technique capable of imaging the distribution of superparamagnetic particles at high spatial and temporal resolution. For the reconstruction of the particle distribution, a system of linear equations has to be solved. The mathematical solution to this linear system can be obtained using a least-squares approach. In this paper, it is shown that the quality of the least-squares solution can be improved by incorporating a weighting matrix using the reciprocal of the matrix-row energy as weights. A further benefit of this weighting is that iterative algorithms, such as the conjugate gradient method, converge rapidly yielding the same image quality as obtained by singular value decomposition in only a few iterations. Thus, the weighting strategy in combination with the conjugate gradient method improves the image quality and substantially shortens the reconstruction time. The performance of weighting strategy and reconstruction algorithms is assessed with experimental data of a 2D MPI scanner.
173 citations
TL;DR: For the first time, the system function is calculated using a model of the signal chain and allows for reconstruction of the particle distribution in a 1-D MPI experiment, enabling fast generation of system functions on arbitrarily dense grids.
Abstract: Magnetic particle imaging (MPI) is a new imaging modality capable of imaging distributions of superparamagnetic nanoparticles with high sensitivity, high spatial resolution and, in particular, high imaging speed. The image reconstruction process requires a system function, describing the mapping between particle distribution and acquired signal. To date, the system function is acquired in a tedious calibration procedure by sequentially measuring the signal of a delta sample at the positions of a grid that covers the field of view. In this work, for the first time, the system function is calculated using a model of the signal chain. The modeled system function allows for reconstruction of the particle distribution in a 1-D MPI experiment. The approach thus enables fast generation of system functions on arbitrarily dense grids. Furthermore, reduction in memory requirements may be feasible by generating parts of the system function on the fly during reconstruction instead of keeping the complete matrix in memory.
168 citations