Christian Kaethner

Magnetic particle imaging: current developments and future directions

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.

On the formulation of the image reconstruction problem in magnetic particle imaging.

Abstract In magnetic particle imaging (MPI), the spatial distribution of magnetic nanoparticles is determined by applying various static and dynamic magnetic fields. Due to the complex physical behavior of the nanoparticles, it is challenging to determine the MPI system matrix in practice. Since the first publication on MPI in 2005, different methods that rely on measurements or simulations for the determination of the MPI system matrix have been proposed. Some methods restrict the simulation to an idealized model to speed up data reconstruction by exploiting the structure of an idealized MPI system matrix. Recently, a method that processes the measurement data in x-space rather than frequency space has been proposed. In this work, we compare the different approaches for image reconstruction in MPI and show that the x-space and the frequency space reconstruction techniques are equivalent.

Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves

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.

Efficient gradient field generation providing a multi-dimensional arbitrary shifted field-free point for magnetic particle imaging

Magnetic Particle Imaging (MPI) is a tomographic imaging modality capable to visualize tracers using magnetic fields. A high magnetic gradient strength is mandatory, to achieve a reasonable image quality. Therefore, a power optimization of the coil configuration is essential. In order to realize a multi-dimensional efficient gradient field generator, the following improvements compared to conventionally used Maxwell coil configurations are proposed: (i) curved rectangular coils, (ii) interleaved coils, and (iii) multi-layered coils. Combining these adaptions results in total power reduction of three orders of magnitude, which is an essential step for the feasibility of building full-body human MPI scanners.

Using data redundancy gained by patch overlaps to reduce truncation artifacts in magnetic particle imaging.

The imaging technology magnetic particle imaging allows the detection of magnetic material, in particular superparamagnetic nanoparticles, by remagnetization of the material via magnetic fields. The application is aimed at medical imaging where the particles are applied as tracer directly into the blood stream. Medical safety considerations such as peripheral nerve stimulation limit the maximal amplitude of the magnetic fields and in turn the field of view size. To handle this constraint the concept of patches was introduced, which allows a shift of a field of view to different positions in order to enlarge the imaging area. If this is done statically an overlap of patches can be used to reduce truncation artifacts occurring at the adjacent edges. In this contribution, a differentiation of two different kinds of patch overlaps, i.e. a trajectory and a system matrix overlap, is made. Further, different concepts to combine the resulting redundant information are investigated with respect to the reduction of truncation artifacts. The methods are analyzed in detail in a simulation study and validated on experimental data.

Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging Based on Lissajous Node Points

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.

Axially Elongated Field-Free Point Data Acquisition in Magnetic Particle Imaging

The magnetic particle imaging (MPI) technology is a new imaging technique featuring an excellent possibility to detect iron oxide based nanoparticle accumulations in vivo. The excitation of the particles and in turn the signal generation in MPI are achieved by using oscillating magnetic fields. In order to realize a spatial encoding, a field-free point (FFP) is steered through the field of view (FOV). Such a positioning of the FFP can thereby be achieved by mechanical or electromagnetical movement. Conventionally, the data acquisition path is either a planar 2-D or a 3-D FFP trajectory. Assuming human applications, the size of the FOV sampled by such trajectories is strongly limited by heating of the body and by nerve stimulations. In this work, a new approach acquiring MPI data based on the axial elongation of a 2-D FFP trajectory is proposed. It is shown that such an elongation can be used as a data acquisition path to significantly increase the acquisition speed, with negligible loss of spatial resolution.

Asymmetric Scanner Design for Interventional Scenarios in Magnetic Particle Imaging

Magnetic particle imaging is an imaging modality that acquires quantitative information about the spatial distribution of magnetic nanoparticles. In combination with an excellent spatial and temporal resolution and due to the fact that no harmful radiation is used, the imaging technique offers possibilities with respect to medical application. As such, interventional scenarios, where it is mandatory to visualize the used instruments, are a perfectly suitable area of application. This paper describes the results of a feasibility study where a novel single-sided coil arrangement based on approximated elliptical coils is designed to be integrated into a patient table. Using such coils perfectly matches the requirements of good patient access, large field of view (FOV), and available space in the table. A small change in the aspect ratio leads to an enlarged FOV with sufficient gradient strength in all directions.

Approximated elliptical coils in magnetic particle imaging

The paper presented results of simulated and measured magnetic fields of an approximated elliptical coil. The simulation values are coincided with the measurement values. Using the relative error as difference metric, the difference between simulation and measurement is presented as well. The visual comparison between the images as well as the resulting values of the relative error show only a minimal difference in the inner zone of the coils. The gradient values for the prototype coil arrangement for x, y and z direction were also shown. With an increasing side length the gradients in x and y direction decrease, while the gradient in z direction slightly increases.

Phantom simulation based on measured gradient fields of a single-sided MPI scanner

Figure 2 shows the reconstruction result using a simulated selection field and a simulated drive field. The resolution of the reconstruction decreases with the distance to the coil assembly of the single-sided scanner. This result will be used to verify later results.