Magnetic Field Characterization

Each Magnetic Particle Imaging Scanner has individual magnetic field profiles with distortions that cannot always be simulated.  In particular, eddy current distortions caused by conductive material in the vicinity of the field generating coils is difficult to simulate. Many MPI areas benefit from characterization of the magnetic field: The most basic advantage is to get a rough estimate for the field-of-view (FOV), as a combination of the drive field and the gradient field. From a hardware point of view, the drive-field profile can be used to manufacture optimized dedicated receive coils, as in "Design of a head coil for high resolution mouse brain perfusion imaging using magnetic particle imaging". For a successful model-based reconstruction that utilizes an artificial generated system matrix, the input parameters to generate the system matrix are particularly important. In "Model-based Calibration and Image Reconstruction with Immobilized Nanoparticles" it was shown that besides a robust particle model and the MPI transfer function, accurate magnetic field values are necessary to describe the scanner dependent measurement signal. Additionally, knowledge about the magnetic field profiles can be used to reduce the number of multi-patch system-matrix measurements as in "Generalized MPI Multi-Patch Reconstruction using Clusters of similar System Matrices".

Generally, the magnetic fields in MPI can be separated into "static" and "dynamic" fields. Other than the "static" fields (gradient and focus fields) that can be measured by a Hall probe, the "dynamic" fields (drive fields) can be measured using a coil sensor and Faradays law of induction. To obtain accurate field profiles, the FOV can be measured in form of a system matrix. However, since magnetic fields satisfy the Laplace equations, they can be expressed within a sphere as a series of spherical harmonic functions by integrating solely over the surface of the sphere. Efficient determination of the coefficients of this expansion can be achieved with the help of a comparatively small number of measurements obtained from spherical t-designs, as shown in "Unique Compact Representation of Magnetic Fields using Truncated Solid Harmonic Expansions". This method was used in "Flexible Selection Field Generation using Iron Core Coil Arrays" to investigate the complex relation between currents of iron core coils and the generated magnetic field. Utilizing a coil sensor, the drive field profile can be measured using the scanners own analog-to-digital converter, shown in "Efficient 3D Drive-Field Characterization for Magnetic Particle Imaging Systems".

A horizontal and vertical field-free line measured inside our Low-Power Iron Magnetic Field Generator.

Publications

[132355]
Title: Generalized MPI Multi-Patch Reconstruction using Clusters of similar System Matrices.
Written by: M. Boberg, T. Knopp, P. Szwargulski, and M. Möddel
in: <em>IEEE Transactions on Medical Imaging</em>. May (2020).
Volume: <strong>39</strong>. Number: (5),
on pages: 1347-1358
Chapter:
Editor:
Publisher:
Series:
Address:
Edition:
ISBN:
how published:
Organization:
School:
Institution:
Type:
DOI: 10.1109/TMI.2019.2949171
URL: https://arxiv.org/abs/2205.01083
ARXIVID:
PMID:

[www]

Note: article, multi-patch, artifact, magneticfield, openaccess

Abstract: 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.