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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. [ABSTRACT FROM AUTHOR]

Magnetic particle imaging visualizes the spatial distribution of superparamagnetic nanoparticles. Because of its key features of excellent sensitivity, high temporal and spatial resolution and biocompatibility of the tracer material it can be used in multiple medical imaging applications. The common reconstruction technique for Lissajous-type trajectories uses a system matrix that has to be previously acquired in a time-consuming calibration scan, leading to long downtimes of the scanning device. In this work, the system matrix is determined by a hybrid approach. Using the hybrid system matrix for reconstruction, the calibration downtime of the scanning device can be neglected. Furthermore, the signal to noise ratio of the hybrid system matrix is much higher, since the size of the required nanoparticle sample can be chosen independently of the desired voxel size. As the signal to noise ratio influences the reconstruction process, the resulting images have better resolution and are less affected by artefacts. Additionally, a new approach is introduced to address the background signal in image reconstruction. The common technique of subtraction of the background signal is replaced by extending the system matrix with an entry that represents the background. It is shown that this approach reduces artefacts in the reconstructed images. [ABSTRACT FROM AUTHOR]

Magnetic particle spectrometry (MPS) is an excellent and straight forward method to determine the response of magnetic nanoparticles to an oscillating magnetic field. Such fields are applied in magnetic particle imaging (MPI). However, state of the art MPS devices lack the ability to excite particles in multidimensional field sequences that are present in MPI devices. Especially the particle behavior caused by Lissajous sequences cannot be measured with only one excitation direction. This work presents a new kind of MPS which features two excitation directions to overcome this limitation. Both field coils can drive AC as well as DC currents and are thereby able to emulate the field sequences for arbitrary spatial positions inside an MPI device. Since the DC currents can be switched very fast, the device can be used as system calibration unit and acquire system matrices in very short time. These are crucial for MPI image reconstruction. As the signal-to-noise-ratio provided by the MPS is approximately 1000 times higher than that of actual imaging devices, the time space analysis of particle signals is more precise and easier done. Four system matrices are presented in this paper which have been measured with the realized multidimensional MPS. Additionally, a time space comparison of the particle signal for Lissajous, radial and spiral trajectories is given. [ABSTRACT FROM AUTHOR]

In magnetic particle imaging, scanners use different spatial sampling techniques to cover the field of view (FOV). As spatial encoding is realized by a selective low field region (a field-free-point, or field-free-line), this region has to be moved through the FOV on specific sampling trajectories. To achieve these trajectories complex time dependent magnetic fields are necessary. Due to the superposition of the selection field and the homogeneous time dependent fields, particles at different spatial positions experience different field sequences. As a result, the dynamic behaviour of those particles can be strongly spatially dependent. So far, simulation studies that determined the trajectory quality have used the Langevin function to model the particle response. This however, neglects the dynamic relaxation of the particles, which is highly affected by magnetic anisotropy. More sophisticated models based on stochastic differential equations that include these effects were only used for one dimensional excitation. In this work, a model based on stochastic differential equations is applied to two-dimensional trajectory field sequences, and the effects of these field sequences on the particle response are investigated. The results show that the signal of anisotropic particles is not based on particle parameters such as size and shape alone, but is also determined by the field sequence that a particle ensemble experiences at its spatial position. It is concluded, that the particle parameters can be optimized in terms of the used trajectory. [ABSTRACT FROM AUTHOR]

Magnetic particle imaging is a tracer-based imaging method that utilizes the non-linear magnetization response of iron-oxide for determining their spatial distribution. The method is based on a sampling scheme where a sensitive spot is moved along a trajectory that captured a predefined field-of-view (FOV). However, particles outside the FOV also contribute to the measurement signal due to their rotation and the non-sharpness of the sensitive spot. In the present work we investigate artifacts that are induced by particles not covered by the FOV and show that the artifacts can be mitigated by using a system matrix that covers not only the region of interest but also a certain area around the FOV. The findings are especially relevant when using a multi-patch acquisition scheme where the boundaries of neighboring patches have to be handled. [ABSTRACT FROM AUTHOR]

The dynamical behaviour of superparamagnetic iron oxide nanoparticles (SPIONs) is not yet fully understood. In magnetic particle imaging (MPI) SPIONs are used to determine quantitative real-time medical images of a tracer material distribution. For reaching spatial resolution in the sub-millimetre range, MPI requires a well engineered instrumentation providing a magnetic field gradient exceeding 2 T m. However, as the particle performance strongly affects the sensitivity of the imaging process, optimization of the particle parameters is a crucial factor, which is not easy to address. Today most simulations of MPI use the Langevin model to describe the particle behaviour. In equilibrium, the model matches the measured data. If alternating fields in the mid kHz frequency range are applied, the dynamic behaviour of the particles differs from the Langevin theory due to anisotropy effects, particle–particle-interactions and/or exchange interaction in case of multi-core particles. In this paper a model based on previous work is introduced, which was adopted to include crystal and shape anisotropy of immobilised mono-domain single-core particles. The model is applied to typical MPI frequencies and field strengths with different possible superposition of the anisotropy effects, leading to differences in the particle response. It is shown that, despite comparatively high anisotropy constants, the magnetocrystalline anisotropy energy does not quench the signal response for MPI. The constructive superposition of shape and crystal anisotropy leads to the best performance in terms of sensitivity and resolution of the associated imaging modality and slightly reduces the energy barriers compared to a sole-shape anisotropy. [ABSTRACT FROM AUTHOR]

Magnetic particle imaging (MPI) is a tomographic imaging modality sensitive to the spatial distribution of magnetic particles. The spectrometer, described in this paper, is capable of measuring the remagnetization spectrum of superparamagnetic nanoparticles. With this spectrometer the suitability of particles, for MPI, can be characterized. Furthermore, the spectrometer can be used to estimate the particle size distribution, which allows for more accurate simulations in MPI. [ABSTRACT FROM AUTHOR]

Magnetic particle imaging (MPI) is a new medical imaging technique visualizing the concentration distribution of superparamagnetic nanoparticles used as tracer material. MPI is not yet in clinical routine, since one of the challenges is the upscaling of scanners. Typically, the magnetic fields of MPI scanners are generated electromagnetically, resulting in an immense power consumption but providing high flexibility in terms of adjusting the field strengths and very fast image acquisition rates. Permanent magnets provide high flux densities and do not need any power supply. However, the flux density is not adjustable, and a mechanical movement is slow compared to electromagnetically varying fields. The MPI scanner concept proposed here uses permanent magnets and provides high flexibility, with the possibility to choose between fast overview scanning and detailed image acquisition. By mechanical rotation of magnetic rings in Halbach array configuration, it is possible to adjust the field or gradient strengths. The latter allows for determining the spatial resolution and the size of the field of view. A continuous mechanical rotation defines the coarseness of the scanning trajectory and image acquisition rate. This concept provides a comparable flexibility, as an alternating magnetic field and an adjustable field gradient can be applied as known from electromagnetically driven MPI systems, and therefore yields high potential for an enlarged system. We present the idea of an arrangement of Halbach arrays and how to calculate the generated magnetic fields. Simulations for an exemplary geometry are provided to show the potential of the proposed setup.