Alexander Weber

Sparse Reconstruction of the Magnetic Particle Imaging System Matrix

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 often with only marginal loss of image quality.

System Characterization of a Highly Integrated Preclinical Hybrid MPI-MRI Scanner

Magnetic particle imaging (MPI) is a novel tracer-based in vivo imaging modality allowing quantitative measurements of the spatial distributions of superparamagnetic iron oxide (SPIO) nanoparticles in three dimensions (3D) and in real time using electromagnetic fields. However, MPI lacks the detection of morphological information which makes it difficult to unambiguously assign spatial SPIO distributions to actual organ structures. To compensate for this, a preclinical highly integrated hybrid system combining MPI and Magnetic Resonance Imaging (MRI) has been designed and gets characterized in this work. This hybrid MPI-MRI system offers a high grade of integration with respect to its hard- and software and enables sequential measurements of MPI and MRI within one seamless study and without the need for object repositioning. Therefore, time-resolved measurements of SPIO distributions acquired with MPI as well as morphological and functional information acquired with MRI can be combined with high spatial co-registration accuracy. With this initial phantom study, the feasibility of a highly integrated MPI-MRI hybrid systems has been proven successfully. This will enable dual-modal in vivo preclinical investigations of mice and rats with high confidence of success, offering the unique feature of precise MPI FOV planning on the basis of MRI data and vice versa.

Local System Matrix Compression for Efficient Reconstruction in Magnetic Particle Imaging

Magnetic particle imaging (MPI) is a quantitative method for determining the spatial distribution of magnetic nanoparticles, which can be used as tracers for cardiovascular imaging. For reconstructing a spatial map of the particle distribution, the system matrix describing the magnetic particle imaging equation has to be known. Due to the complex dynamic behavior of the magnetic particles, the system matrix is commonly measured in a calibration procedure. In order to speed up the reconstruction process, recently, a matrix compression technique has been proposed that makes use of a basis transformation in order to compress the MPI system matrix. By thresholding the resulting matrix and storing the remaining entries in compressed row storage format, only a fraction of the data has to be processed when reconstructing the particle distribution. In the present work, it is shown that the image quality of the algorithm can be considerably improved by using a local threshold for each matrix row instead of a global threshold for the entire system matrix.

Edge Preserving and Noise Reducing Reconstruction for Magnetic Particle Imaging

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.

Artifact free reconstruction with the system matrix approach by overscanning the field-free-point trajectory in magnetic particle imaging.

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.

First 3D dual modality phantom measurements of a hybrid MPI-MRI system using a resistive 12 channel MPI-MRI magnet design

Despite the capability of Magnetic Particle Imaging (MPI) systems [1] to measure spatial distributions of superparamagnetic iron-oxide (SPIO) tracer particles quantitatively with very high temporal resolution, MPI data lack morphological and functional information. To compensate for this, in 2013 combinations of MPI and Magnetic Resonance Imaging (MRI) were proposed as preclinical hybrid MPI-MRI system with integrated dual-operation magnet coils [2] [3]. An alternative approach uses an Travelling Wave MPI insert for a stand-alone pre-polarized low field MRI system [4]. Image fusion of morphological/functional MRI data with complementary MPI data facilitates distinct insight in the pathways and distribution of the administered SPIOs. Hybrid data fusion with high spatial confidence is a basic prerequisite for accurate analysis of in vivo studies. This precision can be achieved optimally only with a hybrid scanner approach featuring integrated dual-operation magnet coils which omits any subject repositioning between MPI and MRI scans.

Symmetries of the 2D magnetic particle imaging system matrix

In magnetic particle imaging (MPI), the relation between the particle distribution and the measurement signal can be described by a linear system of equations. For 1D imaging, it can be shown that the system matrix can be expressed as a product of a convolution matrix and a Chebyshev transformation matrix. For multidimensional imaging, the structure of the MPI system matrix is not yet fully explored as the sampling trajectory complicates the physical model. It has been experimentally found that the MPI system matrix rows have symmetries and look similar to the tensor products of Chebyshev polynomials. In this work we will mathematically prove that the 2D MPI system matrix has symmetries that can be used for matrix compression.

Reconstruction of the Magnetic Particle Imaging System Matrix Using Symmetries and Compressed Sensing

Magnetic particle imaging (MPI) is a tomographic imaging technique that allows the determination of the 3D spatial distribution of superparamagnetic iron oxide nanoparticles. Due to the complex dynamic nature of these nanoparticles, a time-consuming calibration measurement has to be performed prior to image reconstruction. During the calibration a small delta sample filled with the particle suspension is measured at all positions in the field of view where the particle distribution will be reconstructed. Recently, it has been shown that the calibration procedure can be significantly shortened by sampling the field of view only at few randomly chosen positions and applying compressed sensing to reconstruct the full MPI system matrix. The purpose of this work is to reduce the number of necessary calibration scans even further. To this end, we take into account symmetries of the MPI system matrix and combine this knowledge with the compressed sensing method. Experiments on 2D MPI data show that the combination of symmetry and compressed sensing allows reducing the number of calibration scans compared to the pure compressed sensing approach by a factor of about three.

Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

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.

Generic multi-purpose multi-modality phantom kit design

Phantoms are well-established tools for the characterization of imaging systems with regard to resolution, sensitivity, geometric distortions, or flow detection [1]. For the MPI community, the availability of standard phantoms is highly desirable to facilitate direct comparisons between the different MPI scanner designs that have emerged since the inception of this novel imaging modality [2-7]. To be stable over longer times, such phantoms require a sealed containment for liquid contrast agents to prevent leakage or solvent evaporation. As MPI typically requires a second modality for providing morphological reference, it is desirable to use phantoms that also exhibit a good contrast in other modalities such as MRI or μCT. As the spatial resolution of MPI scanners is typically anisotropic, it is desirable to allow different phantom alignments. In this study, we evaluate our new generic kit for building compact phantoms that meet the above requirements.