Abstract. Various imaging modalities allow for time-dependent image reconstructions from measurements where its acquisition also has a time-dependent nature. Magnetic particle imaging (MPI) falls into this class of imaging modalities and it thus also provides a dynamic inverse problem. Without proper consideration of the dynamic behavior, motion artifacts in the reconstruction become an issue. More sophisticated methods need to be developed and applied to the reconstruction of the time-dependent sequences of images. In this context, we investigate the incorporation of motion priors in terms of certain flow-parameter-dependent PDEs in the reconstruction process of time-dependent three dimensional (3D) images in magnetic particle imaging. The present work comprises the method development for a general 3D+time setting for time-dependent linear forward operators, analytical investigation of necessary properties in the MPI forward operator, modeling aspects in dynamic MPI, and extensive numerical experiments on 3D+time imaging including simulated data as well as measurements from a rotation phantom and in vivo data from a mouse.

Magnetic particle imaging exploits the non-linear magnetization of superparamagnetic iron-oxide particles to generate a tomographic image in a defined field-of-view. For reconstruction of the particle distribution, a time-consuming calibration step is required, in which system matrices get measured using a robot. To achieve artifact-free images, system matrices need to cover not only the field-of-view but also a larger area around it. Especially for large measurements- inevitable for future clinical application- this leads to long calibration time and high consumption of persistent memory. In this work, we analyze the signal in the outer part of the system matrix and motivate the usage of extrapolation methods to computationally expand the system matrix after restricting the calibration to the field-of-view. We propose a suitable extrapolation method and show its applicability on measured 2D and 3D data. In doing so, we achieve a considerable reduction of calibration time and consumption of persistent memory while preserving an artifact-free result.

Vascular interventions are a promising application of Magnetic Particle Imaging enabling a high spatial and temporal resolution without using ionizing radiation. The possibility to visualize the vessels as well as the devices, especially at the same time using multi-contrast approaches, enables a higher accuracy for diagnosis and treatment of vascular diseases. Different techniques to make devices MPI visible have been introduced so far, such as varnish markings or filling of balloons. However, all approaches include challenges for in vivo applications, such as the stability of the varnishing or the visibility of tracer filled balloons in deflated state. In this contribution, we present for the first time a balloon catheter that is molded from a granulate incorporating nanoparticles and can be visualized sufficiently in MPI. Computed tomography is used to show the homogeneous distribution of particles within the material. Safety measurements confirm that the incorporation of nanoparticles has no negative effect on the balloon. A dynamic experiment is performed to show that the inflation as well as deflation of the balloon can be imaged with MPI.

Improving resolution and sensitivity will widen possible medical applications of magnetic particle imaging. Pulsed excitation promises such benefits, at the cost of more complex hardware solutions and restrictions on drive field amplitude and frequency. State-of-the-art systems utilize a sinusoidal excitation to drive superparamagnetic nanoparticles into the non-linear part of their magnetization curve, which creates a spectrum with a clear separation of direct feed-through and higher harmonics caused by the particles response. One challenge for rectangular excitation is the discrimination of particle and excitation signals, both broad-band. Another is the drive-field sequence itself, as particles that are not placed at the same spatial position, may react simultaneously and are not separable by their signal phase or shape. To overcome this potential loss of information in spatial encoding for high amplitudes, a superposition of shifting fields and drive-field rotations is proposed in this work. Upon close view, a system matrix approach is capable to maintain resolution, independent of the sequence, if the response to pulsed sequences still encodes information within the phase. Data from an Arbitrary Waveform Magnetic Particle Spectrometer with offsets in two spatial dimensions is measured and calibrated to guarantee device independence. Multiple sequence types and waveforms are compared, based on frequency space image reconstruction from emulated signals, that are derived from measured particle responses. A resolution of 1.0 mT (0.8 mm for a gradient of (−1.25,−1.25,2.5) Tm−1) in x- and y-direction was achieved and a superior sensitivity for pulsed sequences was detected on the basis of reference phantoms.

Background signals are a primary source of artifacts in magnetic particle imaging and limit the sensitivity of the method since background signals are often not precisely known and vary over time. The state-of-the art method for handling background signals uses one or several background calibration measurements with an empty scanner bore and subtracts a linear combination of these background measurements from the actual particle measurement. This approach yields satisfying results in case that the background measurements are taken in close proximity to the particle measurement and when the background signal drifts linearly. In this work, we propose a joint estimation of particle distribution and background signal based on a dictionary that is capable of representing typical background signals. Reconstruction is performed frame-by-frame with minimal assumptions on the temporal evolution of background signals. Thus, even non-linear temporal evolution of the latter can be captured. Using a singular-value decomposition, the dictionary is derived from a large number of background calibration scans that do not need to be recorded in close proximity to the particle measurement. The dictionary is sufficiently expressive and represented by its principle components. The proposed joint estimation of particle distribution and background signal is expressed as a linear Tikhonov-regularized least squares problem, which can be efficiently solved. In phantom experiments it is shown that the method strongly suppresses background artifacts and even allows to estimate and remove the direct feed-through of the excitation field.

The tomographic imaging method magnetic particle imaging (MPI) requires a multi-patch approach for capturing large field of views. This approach consists of a continuous or stepwise spatial shift of a small sub-volume of only few cubic centimeters size, which is scanned using one or multiple excitation fields in the kHz range. Under the assumption of ideal magnetic fields, the MPI system matrix is shift invariant and in turn a single matrix suffices for image reconstruction significantly reducing the calibration time and reconstruction effort. For large field imperfections, however, the method can lead to severe image artifacts. In the present work we generalize the efficient multi-patch reconstruction to work under non-ideal field conditions, where shift invariance holds only approximately for small shifts of the sub-volume. Patches are clustered based on a magnetic-field-based metric such that in each cluster the shift invariance holds in good approximation. The total number of clusters is the main parameter of our method and allows to trade off calibration time and image artifacts. The magnetic-field-based metric allows to perform the clustering without prior knowledge of the system matrices. The developed reconstruction algorithm is evaluated on a multi-patch measurement sequence with 15 patches, where efficient multi-patch reconstruction with a single calibration measurement leads to strong image artifacts. Analysis reveals that calibration measurements can be decreased from 15 to 11 with no visible image artifacts. A further reduction to 9 is possible with only slight degradation in image quality.

Magnetic particle imaging is a tracer based imaging technique to determine the spatial distribution of superparamagnetic iron oxide nanoparticles with a high spatial and temporal resolution. Due to physiological constraints, the imaging volume is restricted in size and larger volumes are covered by shifting object and imaging volume relative to each other. This results in reduced temporal resolution, which can lead to motion artifacts when imaging dynamic tracer distributions. A common source of such dynamic distributions are cardiac and respiratory motion in in-vivo experiments, which are in good approximation periodic. We present a raw data processing technique that combines data snippets into virtual frames corresponding to a specific state of the dynamic motion. The technique is evaluated on the basis of measurement data obtained from a rotational phantom at two different rotational frequencies. These frequencies are determined from the raw data without reconstruction and without an additional navigator signal. The reconstructed images give reasonable representations of the rotational phantom frozen in several different states of motion while motion artifacts are suppressed.

Due to peripheral nerve stimulation, the magnetic particle imaging (MPI) method is limited in the maximum applicable excitation-field amplitude. This in turn leads to a limitation of the size of the covered field of view (FoV) to few millimeters. In order to still capture a larger FoV, MPI is capable to rapidly acquire volumes in a multi-patch fashion. To this end, the small excitation volume is shifted through space using the magnetic focus fields. Recently, it has been shown that the individual patches are preferably reconstructed in a joint fashion by solving a single linear system of equations taking the coupling between individual patches into account. While this improves the image quality, it is computationally and memory demanding since the size of the linear system increases in the best case quadratically with the number of patches. In this paper, we will develop a reconstruction algorithm for MPI multi-patch data exploiting the sparsity of the joint system matrix. A highly efficient implicit matrix format allows for rapid on-the-fly calculations of linear algebra operations involving the system matrix. Using this approach, the computational effort can be reduced to a linear dependence on the number of used patches. The algorithm is validated on 3-D multi-patch phantom data sets and shown to reconstruct large data sets with 15 patches in less than 22 s.

The temporal resolution of the tomographic imaging method magnetic particle imaging (MPI) is remarkably high. The spatial resolution is degraded for measured voltage signal with low signal-to-noise ratio, because the regularization in the image reconstruction step needs to be increased for system-matrix approaches and for deconvolution steps in x -space approaches. To improve the signal-to-noise ratio, blockwise averaging of the signal over time can be advantageous. However, since block-wise averaging decreases the temporal resolution, it prevents resolving the motion. In this paper, a framework for averaging motion-corrupted MPI raw data is proposed. The motion is considered to be periodic as it is the case for respiration and/or the heartbeat. The same state of motion is thus reached repeatedly in a time series exceeding the repetition time of the motion and can be used for averaging. As the motion process and the acquisition process are, in general, not synchronized, averaging of the captured MPI raw data corresponding to the same state of motion requires to shift the starting point of the individual frames. For high-frequency motion, a higher frame rate is potentially required. To address this issue, a binning method for using only parts of complete frames from a motion cycle is proposed that further reduces the motion artifacts in the final images. The frequency of motion is derived directly from the MPI raw data signal without the need to capture an additional navigator signal. Using a motion phantom, it is shown that the proposed method is capable of averaging experimental data with reduced motion artifacts. The methods are further validated on in-vivo data from mouse experiments to compensate the heartbeat.

Magnetic particle imaging (MPI) is an emerging medical imaging modality which is based on the non-linear response of magnetic nanoparticles to an applied magnetic field. It is an important feature of MPI that even fast dynamic processes can be captured for 3D volumes. The high temporal resolution in turn leads to large amounts of data which have to be handled efficiently. But as the system matrix of MPI is non-sparse, the image reconstruction gets computationally demanding. Therefore, currently only basic image reconstruction methods such as Tikhonov regularization are used. However, Tikhonov regularization is known to oversmooth edges in the reconstructed image and to have only a limited noise reducing effect. In this work, we develop an efficient edge preserving and noise reducing reconstruction method for MPI. As regularization model, we propose to use the nonnegative fused lasso model, and we devise a discretization that is adapted to the acquisition geometry of the preclinical MPI scanner considered in this work. We develop a customized solver based on a generalized forward-backward scheme which is particularly suitable for the dense and not well-structured system matrices in MPI. Already a non-optimized prototype implementation processes a 3D volume within a few seconds so that processing several frames per second seems amenable. We demonstrate the improvement in reconstruction quality over the state-of-the-art method in an experimental medical setup for an in-vitro angioplasty of a stenosis.

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.

Biomedical applications such as cell tracking and angiography require the detection of low concentrations of superparamagnetic iron oxide nanoparticles (SPIOs) for imaging purposes. Magnetic particle imaging (MPI) is a new technology which enables the quantitative and time-resolved localization of SPIO distributions. However, the minimum concentration at which the SPIOs can be reconstructed with a suitable quality still remains to be investigated. In this work we examine the background signals in raw data that were measured without any SPIOs in the scanner tube. We show that a background subtraction in combination with a frequency cutoff for the dynamic part of the background signal lowers the detection limit for SPIOs in MPI up to a factor of ten. In-vivo mouse experiments show that for early time points from when the tracer enters the vena cava a reconstructed image of sufficient quality can only be obtained when a background subtraction is performed.

Magnetic particle imaging allows to determine the spatial distribution of magnetic nanoparticles in vivo. The system matrix in magnetic particle imaging is commonly acquired in a tedious calibration scan and requires to measure the system response at numerous positions in the field-of-view. In this paper, we propose a method that significantly reduces the number of required calibration scans. It exploits the special structure of the system matrix and applies sparse reconstruction techniques. Experiments show that the number of calibration scans can be reduced by a factor of ten with only marginal loss of image quality.

The magnetic particle imaging method allows for the quantitative determination of spatial distributions of superparamagnetic nanoparticles in vivo. Recently, it was shown that the 1-D magnetic particle imaging process can be formulated as a convolution. Analyzing the width of the convolution kernel allows for predicting the spatial resolution of the method. However, this measure does not take into account the noise of the measured data. Furthermore, it does not consider a reconstruction step, which can increase the resolution beyond the width of the convolution kernel. In this paper, the spatial resolution of magnetic particle imaging is investigated by analyzing the modulation transfer function of the imaging process. An expression for the spatial resolution is derived, which includes the noise level and which is validated in simulations and experiments.

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.

Signal dephasing due to field inhomogeneity and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with long readouts suffer from artifacts such as blurring, distortion, and intensity variation. These artifacts can be removed in reconstruction, usually based on separately collected information in form of field and relaxation maps. In this work, a recently proposed gridding-based algorithm for off-resonance correction is extended to also address signal decay. It is integrated into a new fixed-point iteration, which permits the joint estimation of an image and field and relaxation maps from multi-echo acquisitions. This approach is then applied in simulations and in vivo experiments and demonstrated to improve both images and maps. The rapid convergence of the fixed-point iteration in combination with the efficient gridding-based correction promises to render the running time of such a joint estimation acceptable.

Spatial variations of the main field give rise to artifacts in magnetic resonance images if disregarded in reconstruction. With non-Cartesian k-space sampling, they often lead to unacceptable blurring. Data from such acquisitions are usually reconstructed with gridding methods and optionally restored with various correction methods. Both types of methods essentially face the same basic problem of adequately approximating an exponential function to enable an efficient processing with fast Fourier transforms. Nevertheless, they have commonly addressed it differently so far. In the present work, a unified approach is pursued. The principle behind gridding methods is first generalized to nonequispaced sampling in both domains and then applied to field inhomogeneity correction. Three new algorithms, which are compatible with a direct conjugate phase and an iterative algebraic reconstruction, are derived in this way from a straightforward embedding of the data into a higher dimensional space. Their evaluation in simulations and phantom experiments with spiral k-space sampling shows that one of them promises to provide a favorable compromise between fidelity and complexity compared with existing algorithms. Moreover, it allows a simple choice of key parameters involved in approximating an exponential function and a balance between the accuracy of reconstruction and correction.