Magnetic particle imaging (MPI) is a novel imaging method that was first proposed by Gleich and Weizenecker in 2005. Applying static and dynamic magnetic fields, MPI exploits the unique characteristics of superparamagnetic iron oxide nanoparticles (SPIONs). The SPIONs’ response allows a three-dimensional visualization of their distribution in space with a superb contrast, a very high temporal and good spatial resolution. Essentially, it is the SPIONs’ superparamagnetic characteristics, the fact that they are magnetically saturable, and the harmonic composition of the SPIONs’ response that make MPI possible at all. As SPIONs are the essential element of MPI, the development of customized nanoparticles is pursued with the greatest effort by many groups. Their objective is the creation of a SPION or a conglomerate of particles that will feature a much higher MPI performance than nanoparticles currently available commercially. A particle’s MPI performance and suitability is characterized by parameters such as the strength of its MPI signal, its biocompatibility, or its pharmacokinetics. Some of the most important adjuster bolts to tune them are the particles’ iron core and hydrodynamic diameter, their anisotropy, the composition of the particles’ suspension, and their coating. As a three-dimensional, real-time imaging modality that is free of ionizing radiation, MPI appears ideally suited for applications such as vascular imaging and interventions as well as cellular and targeted imaging. A number of different theories and technical approaches on the way to the actual implementation of the basic concept of MPI have been seen in the last few years. Research groups around the world are working on different scanner geometries, from closed bore systems to single-sided scanners, and use reconstruction methods that are either based on actual calibration measurements or on theoretical models. This review aims at giving an overview of current developments and future directions in MPI about a decade after its first appearance.

Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization of the polynomial interpolation theory developed for a node set known as Padua points. With appropriately defined polynomial spaces, we will show that the node points of non-degenerate Lissajous curves allow unique interpolation and can be used for quadrature rules in the bivariate setting. An explicit formula for the Lagrange polynomials allows to compute the interpolating polynomial with a simple algorithmic scheme. Compared to the already established schemes of the Padua and Xu points, the numerical results for the proposed scheme show similar approximation errors and a similar growth of the Lebesgue constant. Mathematics Subject Classification

Magnetic Particle Imaging is a new medical imaging modality, which detects superparamagnetic iron oxide nanoparticles. The particles are excited by magnetic fields. Most scanners have a tube-like measurement field and therefore, both the field of view and the object size are limited. A single-sided scanner has the advantage that the object is not limited in size, only the penetration depth is limited. A single-sided scanner prototype for 1D imaging has been presented in 2009. Simulations have been published for a 2D single-sided scanner and first 1D measurements have been carried out. In this paper, the first 2D single-sided scanner prototype is presented and the first calibration-based reconstruction results of measured 2D phantoms are shown. The field free point is moved on a Lissajous trajectory inside a 30 × 30 mm2 area. Images of phantoms with a maximal distance of 10 mm perpendicular to the scanner surface have been reconstructed. Different cylindrically shaped holes of phantoms have been filled with 6.28 μl undiluted Resovist. After the measurement and image reconstruction of the phantoms, particle volumes could be distinguished with a distance of 2 mm and 6 mm in vertical and horizontal direction, respectively.

Magnetic particle imaging (MPI) is a new medical imaging technique that enables three-dimensional real-time imaging of a magnetic tracer material. Although it is not yet in clinical use, it is highly promising, especially for vascular and interventional imaging. The advantages of MPI are that no ionizing radiation is necessary, its high sensitivity enables the detection of very small amounts of the tracer material, and its high temporal resolution enables real-time imaging, which makes MPI suitable as an interventional imaging technique. As MPI is a tracer-based imaging technique, functional imaging is possible by attaching specific molecules to the tracer material. In the first part of this article, the basic principle of MPI will be explained and a short overview of the principles of the generation and spatial encoding of the tracer signal will be given. After this, the used tracer materials as well as their behavior in MPI will be introduced. A subsequent presentation of selected scanner topologies will show the current state of research and the limitations researchers are facing on the way from preclinical toward human-sized scanners. Furthermore, it will be briefly shown how to reconstruct an image from the tracer materials’ signal. In the last part, a variety of possible future clinical applications will be presented with an emphasis on vascular imaging, such as the use of MPI during cardiovascular interventions by visualizing the instruments. Investigations will be discussed, which show the feasibility to quantify the degree of stenosis and diagnose strokes and traumatic brain injuries as well as cerebral or gastrointestinal bleeding with MPI. As MPI is not only suitable for vascular medicine but also offers a broad range of other possible applications, a selection of those will be briefly presented at the end of the article.

Magnetic Particle Imaging (MPI) is an emerging technology in the field of (pre)clinical imaging. The acquisition of a particle signal is realized along specific sampling trajectories covering a defined field of view (FOV). In a system matrix (SM) based reconstruction procedure, the commonly used acquisition path in MPI is a Lissajous trajectory. Such a trajectory features an inhomogeneous coverage of the FOV, i.e. the center region is sampled less dense than the regions towards the edges of the FOV. Conventionally, the respective SM acquisition and the subsequent reconstruction do not reflect this inhomogeneous coverage. Instead, they are performed on an equispaced grid. The objective of this work is to introduce a sampling grid that inherently features the aforementioned inhomogeneity by using node points of Lissajous trajectories. Paired with a tailored polynomial interpolation of the reconstructed MPI signal, the entire image can be recovered. It is the first time that such a trajectory related non-equispaced grid is used for image reconstruction on simulated and measured MPI data and it is shown that the number of sampling positions can be reduced, while the spatial resolution remains constant.

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Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

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