@article{Foerger2026IEEESensors,
Author = {F. Foerger, M. Boberg, N. Hackelberg, P. Heinisch, K. Ostaszewski, J. Faltinath, P. Suskin, F. Thieben, F. Mohn, P. Jürß, M. Möddel and T. Knopp},
Title = {3-D Magnetic Field Camera With Subsecond Temporal Resolution.},
Journal = {IEEE Sensors Journal.},
Year = {(2026).},
Volume = {26.},
Number = {(1),},
Note = {article},
Doi = {https://doi.org/10.1109/JSEN.2025.3629803},
Url = {https://ieeexplore.ieee.org/document/11244237},
Abstract = {Accurate and efficient volumetric magnetic field measurements are essential for a wide range of applications. Conventional methods are often limited in terms of measurement speed and applicability or suffer from scaling problems at larger volumes. This work presents a proof-of-concept field camera designed to measure magnetic fields within a spherical volume at a frame rate of 10 Hz. The camera features an array of 3-D Hall magnetometers positioned according to a spherical t-design, allowing simultaneous magnetic field data acquisition from the surface of the sphere. The approach enables the efficient representation of all three components of the magnetic field inside the sphere using a sixth-degree polynomial, significantly reducing measurement time compared with sequential methods. This work details the design, calibration, and measurement methods of the field camera. To evaluate its performance, we compare it with a sequential single-sensor measurement by examining a magnetic gradient field. The obtained measurement uncertainties of approximately 1% demonstrate the feasibility of the approach and its potential applicability to a variety of future applications.}
}
@article{Dora:25,
Author = {J. Dora, M. Möddel, S. Flenner, J. Reimers, B. Zeller-Plumhoff, C. G. Schroer, T. Knopp, and J. Hagemann},
Title = {Model-based autofocus for near-field phase retrieval.},
Journal = {Optics Express.},
Year = {(2025).},
Volume = {33.},
Number = {(4),},
Pages = {6641-6657},
Month = {Feb},
Note = {article, openaccess},
Publisher = {Optica Publishing Group:},
Doi = {10.1364/OE.544573},
Url = {https://opg.optica.org/oe/abstract.cfm?URI=oe-33-4-6641},
Abstract = {The phase problem is a well known ill-posed reconstruction problem of coherent lens-less microscopic imaging, where only the intensities of a complex wave-field are measured by the detector and the phase information is lost. For the reconstruction of sharp images from holograms in a near-field experimental setting, it is crucial to solve the autofocus problem, i.e., to precisely estimate the Fresnel number of the forward model. Otherwise, blurred out-of focus images that also can contain artifacts are the result. In general, a simple distance measurement at the experiment is not sufficiently accurate, thus the fine-tuning of the Fresnel number has to be done prior to the actual reconstructions. This can be done manually or automatically by an estimation algorithm. To automatize the process, as needed, e.g., for in-situ/operando experiments, different focus criteria have been widely studied in literature but are subjected to certain restrictions. The methods often rely on image analysis of the reconstructed image, making them sensitive to image noise and also neglecting algorithmic properties of the applied phase retrieval. In this paper, we propose a novel criterion, based on a model-matching approach, which improves autofocusing by also taking the underlying reconstruction algorithm, the forward model and the measured hologram into account. We derive a common autofocusing framework, based on a recent phase-retrieval approach and a downhill-simplex method for the automatic optimization of the Fresnel number. We further demonstrate the robustness of the framework on different data sets obtained at the nano imaging endstation of P05 at PETRA III (DESY, Hamburg) operated by Helmholtz-Zentrum Hereon.}
}
@article{Faltinath2025natural,
Author = {J. Faltinath, F. Mohn, F. Foerger, M. Möddel, and T. Knopp},
Title = {Natural Frequency Dependence of Magneto-Mechanical Resonators on Magnet Distance.},
Journal = {IEEE Sensors Journal.},
Year = {(2025).},
Volume = {25.},
Number = {(20),},
Pages = {38073-38081},
Note = {article, openaccess, mmr},
Doi = {https://doi.org/10.1109/JSEN.2025.3600007},
Url = {https://ieeexplore.ieee.org/document/11139087},
Abstract = {The precise derivation of physical quantities like temperature or pressure at arbitrary locations is useful in numerous contexts, e.g., medical procedures or industrial process engineering. The novel sensor technology of magneto-mechanical resonators (MMRs), based on the interaction of a rotor and stator permanent magnet, allows for the combined tracking of the sensor position and orientation while simultaneously sensing an external measurand. Hence, the quantity is coupled to the torsional oscillation frequency, e.g., by varying the magnet distance. In this article, we analyze the (deflection angle-independent) natural frequency dependence of MMR sensors on the rotor-stator distance and evaluate the performance of theoretical models. The three presented sensors incorporate magnets of spherical and/or cylindrical geometry and can be operated at adjustable frequencies within the range of 61.9–307.3 Hz. Our proposed method to obtain the natural frequency demonstrates notable robustness to variations in the initial deflection amplitudes and quality factors, resulting in statistical errors on the mean smaller than 0.05%. We find that the distance–frequency relationship is well-described by an adapted dipole model accounting for material and manufacturing uncertainties. Their combined effect can be compensated by an adjustment of a single parameter, which drives the median model deviation generally below 0.2%. Our depicted methods and results are important for the design and calibration process of new sensor types utilizing the MMR technique.}
}
@article{scheffler2025efficient,
Author = {K. Scheffler, L. Meyn, F. Foerger, M. Boberg, M. Möddel, and T. Knopp},
Title = {Efficient measurement and representation of magnetic fields in tomographic imaging using ellipsoidal harmonics.},
Journal = {Communications Physics.},
Year = {(2025).},
Volume = {8.},
Number = {(112),},
Month = {January},
Note = {article, openaccess, magneticfield},
Publisher = {Nature:},
Doi = {10.1038/s42005-025-02012-5},
Keywords = {magnetic resonance imaging, magnetic particle imaging, magneticfield
},
Abstract = {Given the pivotal role of magnetic fields in modern medicine, there is an increasing necessity for a precise characterization of their strength and orientation at high spatial and temporal resolution. As source-free magnetic fields present in tomographic imaging can be described by harmonic polynomials, they can be efficiently represented using spherical harmonic expansions, which allows for measurement at a small set of points on a sphere surrounding the field of view. However, the majority of closed-bore systems possess a cylindrical field of view, making a sphere an inadequate choice for coverage. Ellipsoids represent a superior geometrical choice, and the theory of ellipsoidal harmonic expansions can be applied to magnetic fields in an analogous manner. Despite the mathematical principles underpinning ellipsoidal harmonics being well-established, their utilization in practical applications remains relatively limited. In this study, we present an effective and flexible approach to measuring and representing magnetic fields present in tomographic imaging, which draws upon the theory of ellipsoidal harmonic expansions.}
}
@article{boberg2025SHE,
Author = {M. Boberg, T. Knopp, and M. Möddel},
Title = {Unique compact representation of magnetic fields using truncated solid harmonic expansions.},
Journal = {European Journal of Applied Mathematics.},
Year = {(2025).},
Pages = {1-28},
Month = {Jan},
Note = {article, magneticfield, openaccess},
Doi = {10.1017/S0956792524000883},
Url = {https://www.cambridge.org/core/journals/european-journal-of-applied-mathematics/article/unique-compact-representation-of-magnetic-fields-using-truncated-solid-harmonic-expansions/4654E5547EE13A3894CD42342782231C#article},
Abstract = {Precise knowledge of magnetic fields is crucial in many medical imaging applications such as magnetic resonance imaging (MRI) or magnetic particle imaging (MPI), as they form the foundation of these imaging systems. Mathematical methods are essential for efficiently analysing the magnetic fields in the entire field-of-view. In this work, we propose a compact and unique representation of the magnetic fields using real solid spherical harmonic expansions, which can be obtained by spherical t-designs. To ensure a unique representation, the expansion point is shifted at the level of the expansion coefficients. As an application scenario, these methods are used to acquire and analyse the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as the unique expansion point.}
}
@article{Merbach2025,
Author = {T. Merbach, F. Kexel, J. Faltinath, M. Möddel, M. Schlüter, T. Knopp, F. Mohn},
Title = {Wireless and passive pressure detection using magneto-mechanical resonances in process engineering.},
Journal = {Measurement Science and Technology.},
Year = {(2025).},
Volume = {36.},
Number = {(8),},
Pages = {085109},
Month = {aug},
Note = {article, mmr},
Doi = {10.1088/1361-6501/adf2c8},
Url = {https://dx.doi.org/10.1088/1361-6501/adf2c8},
Abstract = {A custom-developed magneto-mechanical resonator (MMR) for wireless pressure measurement is investigated for potential applications in process engineering. The MMR sensor utilises changes in the resonance frequency caused by pressure on a flexible 3D printed membrane. The thickness of the printed membrane plays a crucial role in determining the performance and sensitivity of MMRs and can be tailored to meet the requirements of specific applications. The study includes static and dynamic measurements to determine the pressure sensitivity and temporal resolution of the sensor. The results show a minimum sensitivity of and are in agreement with theoretical calculations and measurements. The maximum sensor readout frequency is 2 Hz in this study. Additionally, the temperature dependence of the sensor is investigated, revealing a significant dependence of the resonance frequency on temperature. The developed MMR offers a promising and versatile method for precise pressure measurements in process engineering environments.}
}
@article{Foerger2024AIS,
Author = {F. Foerger, M. Boberg, J. Faltinath, T. Knopp, M. Möddel},
Title = {Design and Optimization of a Magnetic Field Generator for Magnetic Particle Imaging with Soft Magnetic Materials.},
Journal = {Advanced Intelligent Systems.},
Year = {(2024).},
Volume = {6.},
Number = {(11),},
Note = {article},
Doi = {https://doi.org/10.1002/aisy.202400017},
Url = {https://advanced.onlinelibrary.wiley.com/doi/full/10.1002/aisy.202400017},
Abstract = {Magnetic field generators are a key component of Magnetic Particle Imaging (MPI) systems, and their power consumption is a major obstacle on the path to human-sized scanners. Despite their importance, a focused discussion of these generators is rare, and a comprehensive description of the design process is currently lacking. This work presents a methodology for the design and optimization of selection field generators operating with soft magnetic materials outside the linear regime in the context of MPI. Key elements are a mathematical model of magnetic field generators, a formalism for defining field sequences, and a relationship between power consumption and field sequence. These are used to define the design space of a field generator given its system requirements and constraints. The design process is then formulated as an optimization problem. Subsequently, this methodology is then utilized to design a new magnetic field generator specifically for cerebral imaging studies. The optimization result outperforms our existing MPI field generator in terms of power consumption and field of view size, providing a proof-of-concept for the entire methodology. As the approach is very general, it can be extended beyond the MPI context to other areas such as magnetic manipulation of medical devices and micro-robotics.}
}
@article{mohn_resonant_2024,
Author = {F. Mohn, F. Foerger, F. Thieben, M. Möddel, I. Schmale, T. Knopp and M. Graeser},
Title = {Resonant Inductive Coupling Network for Human-Sized Magnetic Particle Imaging.},
Journal = {Review of Scientific Instruments.},
Year = {(2024).},
Volume = {95.},
Number = {(4),},
Pages = {044701},
Note = {article, openaccess, brainimager},
Doi = {10.1063/5.0192784},
Keywords = {Mohn},
Abstract = {In magnetic particle imaging, a field-free region is maneuvered throughout the field of view using a time-varying magnetic field known as the drive-field. Human-sized systems operate the drive-field in the kHz range and generate it by utilizing strong currents that can rise to the kA range within a coil called the drive field generator. Matching and tuning between a power amplifier, a band-pass filter, and the drive-field generator is required. Here, for reasons of safety in future human scanners, a symmetrical topology and a transformer called an inductive coupling network are used. Our primary objectives are to achieve floating potentials to ensure patient safety while attaining high linearity and high gain for the resonant transformer. We present a novel systematic approach to the design of a loss-optimized resonant toroid with a D-shaped cross section, employing segmentation to adjust the inductance-to-resistance ratio while maintaining a constant quality factor. Simultaneously, we derive a specific matching condition for a symmetric transmit--receive circuit for magnetic particle imaging. The chosen setup filters the fundamental frequency and allows simultaneous signal transmission and reception. In addition, the decoupling of multiple drive field channels is discussed, and the primary side of the transformer is evaluated for maximum coupling and minimum stray field. Two prototypes were constructed, measured, decoupled, and compared to the derived theory and method-of-moment based simulations.}
}
@article{thieben_system_2024,
Author = {F. Thieben, F. Foerger, F. Mohn, N. Hackelberg, M. Boberg, J.-P. Scheel, Möddel, M. Graeser, and T. Knopp},
Title = {System Characterization of a Human-Sized 3D Real-Time Magnetic Particle Imaging Scanner for Cerebral Applications.},
Journal = {Communications Engineering.},
Year = {(2024).},
Volume = {3.},
Number = {(1),},
Pages = {47},
Note = {article, openaccess, brainimager},
Doi = {10.1038/s44172-024-00192-6},
Keywords = {Mohn},
Abstract = {Abstract Since the initial patent in 2001, the Magnetic Particle Imaging community has endeavored to develop a human-applicable Magnetic Particle Imaging scanner, incorporating contributions from various research fields. Here we present an improved head-sized Magnetic Particle Imaging scanner with low power consumption, operated by open-source software and characterize it with an emphasis on human safety. The focus is on the evaluation of the technical components and on phantom experiments for brain perfusion. We achieved 3D single- and multi-contrast imaging at 4 Hz frame rate. The system characterization includes sensitivity, resolution, perfusion and multi-contrast experiments as well as field measurements and sequence analysis. Images were acquired with a clinically approved tracer and within human peripheral nerve stimulation thresholds. This advanced scanner holds potential as a tomographic imager for diagnosing conditions such as ischemic stroke (different stages) or intracranial hemorrhage in environments lacking electromagnetic shielding, such as the intensive care unit.}
}
@article{Dora:24,
Author = {J. Dora, M. Möddel, S. Flenner, C. G. Schroer, T. Knopp, and J. Hagemann},
Title = {Artifact-suppressing reconstruction of strongly interacting objects in X-ray near-field holography without a spatial support constraint.},
Journal = {Optics Express.},
Year = {(2024).},
Volume = {32.},
Number = {(7),},
Pages = {10801-10828},
Month = {Mar},
Note = {article, openaccess},
Publisher = {Optica Publishing Group:},
Doi = {10.1364/OE.514641},
Url = {https://opg.optica.org/oe/abstract.cfm?URI=oe-32-7-10801},
Abstract = {The phase problem is a well known ill-posed reconstruction problem of coherent lens-less microscopic imaging, where only the squared magnitude of a complex wavefront is measured by a detector while the phase information of the wave field is lost. To retrieve the lost information, common algorithms rely either on multiple data acquisitions under varying measurement conditions or on the application of strong constraints such as a spatial support. In X-ray near-field holography, however, these methods are rendered impractical in the setting of time sensitive in situ and operando measurements. In this paper, we will forego the spatial support constraint and propose a projected gradient descent (PGD) based reconstruction scheme in combination with proper preprocessing and regularization that significantly reduces artifacts for refractive reconstructions from only a single acquired hologram without a spatial support constraint. We demonstrate the feasibility and robustness of our approach on different data sets obtained at the nano imaging endstation of P05 at PETRA III (DESY, Hamburg) operated by Helmholtz-Zentrum Hereon.}
}
@article{Nawwas2024PMB,
Author = {L. Nawwas, M. Möddel and T. Knopp },
Title = {Analysis of leakage artifacts and their impact on convergence of algebraic reconstruction in multi-contrast magnetic particle imaging.},
Journal = {Physics in Medicine & Biology.},
Year = {(2024).},
Volume = {69.},
Number = {(21),},
Pages = {1-15},
Month = {October},
Note = {article, artifact},
Doi = {10.1088/1361-6560/ad7e77},
Url = {https://iopscience.iop.org/article/10.1088/1361-6560/ad7e77},
Keywords = {article},
Abstract = {Objective. Magnetic particle imaging (MPI) is a tracer-based medical imaging modality with great potential due to its high sensitivity, high spatiotemporal resolution, and ability to quantify the tracer concentration. Image reconstruction in MPI is an ill-posed problem, which the use of regularization methods can address. Multi-contrast MPI reconstructs the signal from different tracer materials or environments separately, resulting in multi-channel images that enable quantification of, for example, temperature or viscosity. Single- and multi-contrast MPI reconstructions produce different kinds of artifacts. The objective of this work is threefold: first, to present the concept of multi-contrast specific MPI channel leakage artifacts; second, to ascertain the source of these leakage artifacts; and third, to introduce a method for their reduction. Approach. A definition for leakage artifacts is established, and a quantification method is proposed. A comprehensive analysis is conducted to establish a connection between the properties of the multi-contrast MPI system matrix and the leakage artifacts. Moreover, a two-step measurement and reconstruction method is introduced to reduce channel leakage artifacts between multi-contrast MPI channels. Main results. The severity of these artifacts correlates with the system matrix shape and condition number and depends on the similarity of the corresponding frequency components. Using the proposed two-step method on both semi-simulated and measured data a significant leakage reduction and speed up the convergence of the multi-contrast MPI reconstruction was observed. Significance. The multi-contrast system matrix analysis we conducted is essential for understanding the source of the channel leakage artifacts and finding methods to reduce them. Our proposed two-step method is expected to improve the potential for real-time multi-contrast MPI applications.}
}
@article{mohn2023saline,
Author = {F. Mohn, M. Exner, P. Szwargulski, M. Möddel, T. Knopp, and M. Graeser},
Title = {Saline bolus for negative contrast perfusion imaging in magnetic particle imaging.},
Journal = {Physics in Medicine & Biology.},
Year = {(2023).},
Volume = {68.},
Number = {(17),},
Pages = {5026},
Month = {aug},
Note = {article, openaccess},
Isbn = {0031-9155, 1361-6560},
Doi = {10.1088/1361-6560/ace309},
Keywords = {Mohn},
Abstract = {Magnetic Particle Imaging is capable to measure the spatial distribution of magnetic nanoparticles with high temporal resolution. As a quantitative tracer based imaging method, the signal is linear in the tracer concentration for any location that contains nanoparticles and zero in the surrounding tissue which does not provide any intrinsic signal. After tracer injection, the concentration over time (positive contrast) can be utilized to calculate dynamic diagnostic parameters like perfusion parameters in vessels and organs, which are an important tool in medical diagnosis. Every acquired perfusion image thus requires a new bolus of tracer with a sufficiently large iron dose to be visible above the background. We propose a method, where a bolus of physiological saline solution without any particles (negative contrast) displaces the remaining steady state concentration which in turn contributes to the image contrast. Perfusion parameters are calculated based on the time response of this negative bolus and compared to a positive bolus. Results from phantom experiments show that normalized signals from positive and negative boli are concurrent and deviations of calculated perfusion maps are low. Our method opens up the possibility to increase the total monitoring time of a future patient by utilizing a positive-negative contrast sequence, while minimizing the iron dose per acquired image.}
}
@article{Thieben2023receive,
Author = {F. Thieben, T. Knopp, M. Boberg, F. Foerger, M.Graeser, and M. Möddel},
Title = {On the Receive Path Calibration of Magnetic Particle Imaging Systems.},
Journal = {IEEE Transactions on Instrumentation and Measurement.},
Year = {(2023).},
Volume = {72.},
Pages = {1-15},
Note = {article, instrumentation},
Doi = {10.1109/TIM.2022.3219461},
Url = {https://ieeexplore.ieee.org/document/9939022},
Abstract = {Magnetic nanoparticles are a valuable tool in many biomedical applications and can be used for diagnostic and therapeutic purposes. In magnetic particle imaging (MPI) and magnetic particle spectroscopy (MPS), the particles are subjected to a dynamic magnetic field and the particle magnetization response is simultaneously measured using one or multiple receive coils. Separating the particle signal from the feed-through signal is commonly done by advanced passive filtering, which distorts the particle signal. To correct this distortion, the transfer function of the receive chain needs to be known. While in principle, the transfer function can be simulated, due to imperfections in the electronic components, it is often more accurate to determine the transfer function in a calibration procedure. Although this system calibration, utilizing a calibration-coil setup has been done by several research groups in the past, a general description of the underlying calibration model and methodology is still missing. In this paper we provide a general multi-channel calibration procedure for inductive receive paths in MPI and a blueprint to investigate model and method uncertainties. We generalized the calibration procedure to also cover non-orthogonal and non-homogeneous receive coils. Finally, we showcase the calibration procedure and uncertainty analysis on our custom MPS system and use the MPI transfer functions of misaligned receive coils to decouple their superimposed receive signals from the receive path. The findings enable the comparison of MPI signals from different devices and can be used to normalize measurements and system functions in devices with exchangeable receive coils.}
}
@article{albers2022modeling,
Author = {H. Albers, T. Knopp, M. Möddel, M. Boberg, and T. Kluth},
Title = {Modeling the magnetization dynamics for large ensembles of immobilized magnetic nanoparticles in multi-dimensional magnetic particle imaging.},
Journal = {Journal of Magnetism and Magnetic Materials.},
Year = {(2022).},
Volume = {543.},
Pages = {168534},
Month = {February},
Note = {article, model-based},
Doi = {10.1016/j.jmmm.2021.168534},
Url = {https://arxiv.org/abs/2106.08040},
Abstract = {Magnetic nanoparticles (MNPs) play an important role in biomedical applications including imaging modalities such as magnetic resonance imaging (MRI) and magnetic particle imaging (MPI). The latter one exploits the non-linear magnetization response of a large ensemble of magnetic nanoparticles to magnetic fields which allows determining the spatial distribution of the MNP concentration from measured voltage signals. The image-to-voltage mapping is linear and described by a system matrix. Currently, modeling the voltage signals of large ensembles of MNPs in an MPI environment is not yet accurately possible, especially for liquid tracers in multi-dimensional magnetic excitation fields. As an immediate consequence, the system matrix is still obtained in a time consuming calibration procedure. While the ferrofluidic case can be seen as the typical setting, more recently immobilized and potentially oriented MNPs have received considerable attention. By aligning the particles magnetic easy axis during immobilization one can encode the angle of the particle’s magnetic easy axis into the magnetization response providing a relevant benchmark system for model-based approaches. In this work we address the modeling problem for immobilized and oriented MNPs in the context of MPI. We investigate a model-based approach where the magnetization response is simulated by a Néel rotation model for the particle’s magnetic moments and the ensemble magnetization is obtained by solving a Fokker–Planck equation approach. Since the parameters of the model are a-priori unknown, we investigate different methods for performing a parameter identification and discuss two different models: One where a single function vector is used from the space spanned by the model parameters and another where a superposition of function vectors is considered. We show that our model can much more accurately reproduce the orientation dependent signal response when compared to the equilibrium model, which marks the current state-of-the-art for model-based system matrix simulations in MPI.}
}
@article{Nawwas2021,
Author = {L. Nawwas, C. Brandt, P. Szwargulski, T. Knopp, and M. Möddel},
Title = {Reduction of bias for sparsity promoting regularization in MPI.},
Journal = {International Journal on Magnetic Particle Imaging.},
Year = {(2021).},
Volume = {7.},
Number = {(2),},
Pages = {1-13},
Note = {article, artifact},
Doi = {https://doi.org/10.18416/IJMPI.2021.2112002},
Url = {https://journal.iwmpi.org/index.php/iwmpi/article/view/330},
Keywords = {article},
Abstract = {Magnetic Particle Imaging (MPI) is a tracer based medical imaging modality with great potential due to its high sensitivity, high spatial and temporal resolution, and its ability to quantify the tracer concentration. Image reconstruction in MPI is an ill-posed problem, which can be addressed by regularization methods that lead to a reconstruction bias, which is apparent in a systematic mismatch between true and reconstructed tracer distribution. This is expressed in a background signal, a mismatch of the spatial support of the tracer distribution and a mismatch of its values. In this work, MPI reconstruction bias and its impact are investigated and a recently proposed debiasing method with significant bias reduction capabilities is adopted.}
}
@article{boberg2021dynamicrange,
Author = {M. Boberg, N. Gdaniec, P. Szwargulski, F. Werner, M. Möddel, and T. Knopp},
Title = {Simultaneous imaging of widely differing particle concentrations in MPI: problem statement and algorithmic proposal for improvement.},
Journal = {Physics in Medicine & Biology.},
Year = {(2021).},
Volume = {66.},
Number = {(9),},
Pages = {095004},
Month = {April},
Note = {article, artifact, openaccess},
Doi = {10.1088/1361-6560/abf202},
Url = {https://arxiv.org/abs/2205.01364},
Abstract = {Magnetic Particle Imaging (MPI) is a tomographic imaging technique for determining the spatial distribution of superparamagnetic nanoparticles. Current MPI systems are capable of imaging iron masses over a wide dynamic range of more than four orders of magnitude. In theory, this range could be further increased using adaptive amplifiers, which prevent signal clipping. While this applies to a single sample, the dynamic range is severely limited if several samples with different concentrations or strongly inhomogeneous particle distributions are considered. One scenario that occurs quite frequently in pre-clinical applications is that a highly concentrated tracer bolus in the vascular system shadows nearby organs with lower effective tracer concentrations. The root cause of the problem is the ill-posedness of the MPI imaging operator, which requires regularization for stable reconstruction. In this work, we introduce a simple two-step algorithm that increases the dynamic range by a factor of four. Furthermore, the algorithm enables spatially adaptive regularization, i.e. highly concentrated signals can be reconstructed with maximum spatial resolution, while low concentrated signals are strongly regularized to prevent noise amplification.}
}
@article{PhysRevApplied.16.L041003,
Author = {M. Möddel, F. Griese, T. Kluth, and T. Knopp},
Title = {Estimating the Spatial Orientation of Immobilized Magnetic Nanoparticles with Parallel-Aligned Easy Axes.},
Journal = {Phys. Rev. Applied.},
Year = {(2021).},
Volume = {16.},
Pages = {L041003},
Month = {Oct},
Note = {article, openaccess, multi-contrast},
Publisher = {American Physical Society:},
Doi = {10.1103/PhysRevApplied.16.L041003},
Url = {https://link.aps.org/doi/10.1103/PhysRevApplied.16.L041003}
}
@article{knopp2021efficient,
Author = {T. Knopp, M. Grosser, M. Graeser, T. Gerkmann, and M. Möddel},
Title = {Efficient Joint Estimation of Tracer Distribution and Background Signals in Magnetic Particle Imaging using a Dictionary Approach.},
Journal = {IEEE Transactions on Medical Imaging.},
Year = {(2021).},
Volume = {40.},
Number = {(12),},
Pages = {3568-3579},
Note = {article, artifact},
Doi = {10.1109/TMI.2021.3090928},
Url = {https://arxiv.org/pdf/2006.05741},
Abstract = {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.}
}
@article{Weller2020,
Author = {D. Weller, J. M. Salamon, A. Frölich, M. Möddel, T. Knopp and R. Werner},
Title = {Combining Direct 3D Volume Rendering and Magnetic Particle Imaging to Advance Radiation-Free Real-Time 3D Guidance of Vascular Interventions.},
Journal = {Cardiovascular and interventional radiology.},
Year = {(2020).},
Volume = {43.},
Number = {(2),},
Pages = {322-330},
Month = {February},
Note = {article},
Publisher = {Springer US:},
Url = {https://link.springer.com/article/10.1007/s00270-019-02340-4},
Abstract = {Magnetic particle imaging (MPI) is a novel tomographic radiation-free imaging technique that combines high spatial resolution and real-time capabilities, making it a promising tool to guide vascular interventions. Immediate availability of 3D image data is a major advantage over the presently used digital subtraction angiography (DSA), but new methods for real-time image analysis and visualization are also required to take full advantage of the MPI properties. This laboratory study illustrates respective techniques by means of three different patient-specific 3D vascular flow models.
}
}
@article{Salamon2020,
Author = {J. Salamon, J. Dieckhoff, M. G. Kaul, C. Jung, G. Adam, M. Möddel, T. Knopp, S. Draack, F. Ludwig and H. Ittrich},
Title = {Visualization of spatial and temporal temperature distributions with magnetic particle imaging for liver tumor ablation therapy.},
Journal = {Scientific Reports.},
Year = {(2020).},
Volume = {10.},
Number = {(7480),},
Pages = {1-11},
Month = {May},
Note = {article},
Url = {https://www.nature.com/articles/s41598-020-64280-1},
Abstract = {Temperature-resolved magnetic particle imaging (MPI) represents a promising tool for medical imaging applications. In this study an approach based on a single calibration measurement was applied for highlighting the potential of MPI for monitoring of temperatures during thermal ablation of liver tumors. For this purpose, liver tissue and liver tumor phantoms embedding different superparamagnetic iron oxide nanoparticles (SPION) were prepared, locally heated up to 70?°C and recorded with MPI. Optimal temperature MPI SPIONs and a corresponding linear model for temperature calculation were determined. The temporal and spatial temperature distributions were compared with infrared (IR) camera results yielding quantitative agreements with a mean absolute deviation of 1?°C despite mismatches in boundary areas.}
}
@article{boberg2019generalized,
Author = {M. Boberg, T. Knopp, P. Szwargulski, and M. Möddel},
Title = {Generalized MPI Multi-Patch Reconstruction using Clusters of similar System Matrices.},
Journal = {IEEE Transactions on Medical Imaging.},
Year = {(2020).},
Volume = {39.},
Number = {(5),},
Pages = {1347-1358},
Month = {May},
Note = {article, multi-patch, artifact, magneticfield, openaccess},
Doi = {10.1109/TMI.2019.2949171},
Url = {https://arxiv.org/abs/2205.01083},
Keywords = {calibration;image reconstruction;matrix algebra;medical image processing;tomographic imaging method magnetic particle imaging;stepwise spatial shift;MPI system matrix;image reconstruction;shift invariance;multipatch measurement sequence;image quality;MPI multipatch reconstruction;magnetic-field-based metric;multipatch reconstruction;continuous spatial shift;Image reconstruction;Calibration;Magnetic resonance imaging;Reconstruction algorithms;Atmospheric measurements;Particle measurements;Biomedical imaging;focus fields;image reconstruction;magnetic particle imaging},
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.}
}
@article{gdaniec2020rotation,
Author = {N. Gdaniec, M. Boberg, M. Möddel, P. Szwargulski, and T. Knopp},
Title = {Suppression of Motion Artifacts Caused by Temporally Recurring Tracer Distributions in Multi-Patch Magnetic Particle Imaging.},
Journal = {IEEE Transactions on Medical Imaging.},
Year = {(2020).},
Volume = {39.},
Number = {(11),},
Pages = {3548-3558},
Month = {November},
Note = {article, multi-patch, artifact, opendata, openaccess},
Doi = {10.1109/TMI.2020.2998910},
Url = {https://arxiv.org/abs/2205.01085},
Keywords = {Image reconstruction;Motion artifacts;Dynamics;Phantoms;Spatial resolution;Biomedical imaging;magnetic particle imaging;motion artifacts;motion compensation;motion detection},
Abstract = {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.}
}
@article{ShashaPMB2019,
Author = {C. Shasha, E. Teeman, K. M. Krishnan, P. Szwargulski, T. Knopp, and M. Möddel},
Title = {Discriminating nanoparticle core size using multi-contrast MPI.},
Journal = {Physics in Medicine and Biology.},
Year = {(2019).},
Note = {article, multi-contrast},
Doi = {https://doi.org/10.1088/1361-6560/ab0fc9},
Url = {https://iopscience.iop.org/article/10.1088/1361-6560/ab0fc9},
Abstract = {Magnetic particle imaging (MPI) is an imaging modality that detects the response of a distribution of magnetic nanoparticle tracers to static and alternating magnetic fields. There has recently been exploration into multi-contrast MPI, in which the signal from different tracer materials or environments is separately reconstructed, resulting in multi-channel images that could enable temperature or viscosity quantification. In this work, we apply a multi-contrast reconstruction technique to discriminate between nanoparticle tracers of different core sizes. Three nanoparticle types with core diameters of 21.9nm, 25.3nm, and 27.7nm were each imaged at 21 different locations within the scanner field of view. Multi-channel images were reconstructed for each sample and location, with each channel corresponding to one of the three core sizes. For each image, signal weight vectors were calculated, which were then used to classify each image by core size. With a block averaging length of 10000, the median signal-to-noise ratio was 40 or higher for all three sample types, and a correct prediction rate of 96.7% was achieved, indicating that core size can effectively be predicted using signal weight vector classification with close to 100% accuracy while retaining high MPI image quality.}
}
@article{Weller2019,
Author = {D. Weller, J. M. Salamon, A. Frölich, M. Möddel, T. Knopp, and R. Werner},
Title = {Combining Direct 3D Volume Rendering and Magnetic Particle Imaging to Advance Radiation-Free Real-Time 3D Guidance of Vascular Interventions.},
Journal = {CardioVascular and Interventional Radiology.},
Year = {(2019).},
Month = {Sep},
Note = {article, interventional, real-time},
Doi = {10.1007/s00270-019-02340-4},
Url = {https://doi.org/10.1007/s00270-019-02340-4},
Abstract = {Magnetic particle imaging (MPI) is a novel tomographic radiation-free imaging technique that combines high spatial resolution and real-time capabilities, making it a promising tool to guide vascular interventions. Immediate availability of 3D image data is a major advantage over the presently used digital subtraction angiography (DSA), but new methods for real-time image analysis and visualization are also required to take full advantage of the MPI properties. This laboratory study illustrates respective techniques by means of three different patient-specific 3D vascular flow models.}
}
@article{Graeser2019b,
Author = {M. Graeser, F. Thieben, P. Szwargulski, F. Werner, N. Gdaniec, M. Boberg, F. Griese, M. Möddel, P. Ludewig, D. van de Ven, O.M. Weber, O. Woywode, B. Gleich, and T. Knopp},
Title = {Human-sized Magnetic Particle Imaging for Brain Applications.},
Journal = {Nature Communications.},
Year = {(2019).},
Volume = {10.},
Number = {(1936),},
Pages = {1-9},
Note = {article, brainimager, openaccess},
Doi = {10.1038/s41467-019-09704-x},
Url = {https://www.nature.com/articles/s41467-019-09704-x},
Keywords = {article},
Abstract = {Determining the brain perfusion is an important task for diagnosis of vascular diseases such as occlusions and intracerebral haemorrhage. Even after successful diagnosis, there is a high risk of restenosis or rebleeding such that patients need intense attention in the days after treatment. Within this work, we present a diagnostic tomographic imager that allows access to brain perfusion quantitatively in short intervals. The device is based on the magnetic particle imaging technology and is designed for human scale. It is highly sensitive and allows the detection of an iron concentration of 263 pmol(Fe)/ml, which is one of the lowest iron concentrations imaged by MPI so far. The imager is self-shielded and can be used in unshielded environments such as intensive care units. In combination with the low technical requirements this opens up a variety of medical applications and would allow monitoring of stroke on intensive care units.}
}
@article{SzwargulskiTMI2018a,
Author = {P. Szwargulski, M. Möddel, N. Gdaniec and T. Knopp},
Title = {Efficient Joint Image Reconstruction of Multi-Patch Data reusing a Single System Matrix in Magnetic Particle Imaging.},
Journal = {IEEE Transactions on Medical Imaging.},
Year = {(2019).},
Volume = {38.},
Number = {(4),},
Pages = {932-944},
Month = {April},
Note = {article, multi-patch},
Doi = {10.1109/TMI.2018.2875829},
Url = {https://ieeexplore.ieee.org/document/8490900},
Keywords = {Image reconstruction;Magnetic resonance imaging;Trajectory;Biomedical imaging;Mathematical model;Coils;Biomedical Imaging;Focus fields;Image Reconstruction;Magnetic Particle Imaging},
Abstract = {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 field of view, 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 work, 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 3D multi-patch phantom datasets and shown to reconstruct a large datasets with 15 patches in less than 22 seconds.}
}
@article{latus2019bimodal,
Author = {S. Latus, F. Griese, M. Schlüter, C. Otte, M. Möddel, M. Graeser, T. Saathoff, T. Knopp, and A. Schlaefer},
Title = {Bimodal intravascular volumetric imaging combining OCT and MPI.},
Journal = {Medical Physics.},
Year = {(2019).},
Volume = {46.},
Number = {(3),},
Pages = {1371-1383},
Month = {Mar},
Note = {article},
Doi = {10.1002/mp.13388}
}
@article{knopp2019mpifiles,
Author = {T. Knopp, M. Möddel, F. Griese, F. Werner, P. Szwargulski, N. Gdaniec, and M. Boberg},
Title = {MPIFiles.jl: A Julia Package for Magnetic Particle Imaging Files.},
Journal = {Journal of Open Source Software.},
Year = {(2019).},
Volume = {4.},
Number = {(38),},
Pages = {1331},
Note = {article, opensoftware, openaccess, mpisoftware},
Doi = {https://doi.org/10.21105/joss.01331},
Url = {http://joss.theoj.org/papers/10.21105/joss.01331}
}
@article{Knopp2019MPIReco,
Author = {T. Knopp, P. Szwargulski, F. Griese, M. Grosser, M. Boberg, and M. Möddel},
Title = {MPIReco.jl: Julia Package for Image Reconstruction in MPI.},
Journal = {International Journal on Magnetic Particle Imaging.},
Year = {(2019).},
Volume = {5.},
Number = {(1),},
Pages = {9 pp},
Note = {article, opensoftware, openaccess, mpisoftware},
Doi = {10.18416/ijmpi.2019.1907001},
Keywords = {article}
}
@article{10.1088/1367-2630/aad44b,
Author = {M. Möddel, C. Meins, J. Dieckhoff, and T. Knopp},
Title = {Viscosity quantification using multi-contrast magnetic particle imaging.},
Journal = {New Journal of Physics.},
Year = {(2018).},
Volume = {20.},
Number = {(8),},
Pages = {083001},
Note = {article, multi-contrast, openaccess},
Doi = {10.1088/1367-2630/aad44b},
Url = {http://iopscience.iop.org/article/10.1088/1367-2630/aad44b},
Abstract = {Abstract Magnetic particle imaging (MPI) is a relatively new tomographic imaging technique using static and oscillating magnetic fields to image the spatial distribution of magnetic nanoparticles. The latter being the contrast MPI has been initially designed for. However, recently it has been shown that MPI can be extended to a multi-contrast method that allows to simultaneously image the signals of different MPI tracer materials. Additionally, it has been shown that changes in the particles environment, e.g. the viscosity have an impact on the MPI signal and can potentially be used for functional imaging. The purpose of the present work is twofold. First, we generalize the MPI imaging equation to describe different multi-contrast settings in a unified framework. This allows for more precise interpretation and discussion of results obtained by single- and multi-contrast reconstruction. Second, we propose and validate a method that allows to determine the viscosity of a small sample from a dual-contrast reconstruction. To this end, we exploit a calibration curve mapping the sample viscosity onto the relative signal weights within the channels of the dual-contrast reconstruction. The latter allows us to experimentally determine the viscosity of the particle environment in the range of 1 mPas to 51.8 mPas with a relative methodological error of less than 6%.}
}
@article{SzwargulskiJoMI2018,
Author = {P. Szwargulski, N. Gdaniec, M. Graeser, M. Möddel, F. Griese, K. M. Krishnan, T. M. Buzug, and T. Knopp},
Title = {Moving table magnetic particle imaging: a stepwise approach preserving high spatio-temporal resolution.},
Journal = {Journal of Medical Imaging.},
Year = {(2018).},
Volume = {5.},
Number = {(4),},
Pages = {046002},
Note = {article, multi-patch, openaccess},
Doi = {doi.org/10.1117/1.JMI.5.4.046002},
Url = {https://arxiv.org/abs/1812.04075},
Keywords = {magnetic particle imaging; enlarging the field of view; moving table; multi-patch},
Abstract = {Magnetic particle imaging (MPI) is a highly sensitive imaging method that enables the visualization of magnetic tracer materials with a temporal resolution of more than 46 volumes per second. In MPI, the size of the field of view (FoV) scales with the strengths of the applied magnetic fields. In clinical applications, those strengths are limited by peripheral nerve stimulation, specific absorption rates, and the requirement to acquire images of high spatial resolution. Therefore, the size of the FoV is usually a few cubic centimeters. To bypass this limitation, additional focus fields and/or external object movements can be applied. The latter approach is investigated. An object is moved through the scanner bore one step at a time, whereas the MPI scanner continuously acquires data from its static FoV. Using a 3-D phantom and dynamic 3-D in vivo data, it is shown that the data from such a moving table experiment can be jointly reconstructed after reordering the data with respect to the stepwise object shifts and heart beat phases.}
}
@article{2016arXiv160206072K,
Author = {T. Knopp, T. Viereck, G. Bringout, M. Ahlborg, A. von Gladiss, C. Kaethner, A. Neumann, P. Vogel, J. Rahmer, M. Möddel},
Title = {MDF: Magnetic Particle Imaging Data Format.},
Journal = {ArXiv e-prints.},
Year = {(2018).},
Volume = {1602.06072v6.},
Pages = {1-15},
Month = {jan},
Note = {article, MDF},
Url = {http://arxiv.org/abs/1602.06072v6}
}
@article{Erb2018Mathematical,
Author = {W. Erb, A. Weinmann, M. Ahlborg, C. Brandt, G. Bringout, T. M. Buzug, J. Frikel, C. Kaethner, T. Knopp, T. März, M. Möddel, M. Storath, and A. Weber},
Title = {Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging.},
Journal = {Inverse Problems.},
Year = {(2018).},
Pages = {to appear},
Note = {article},
Keywords = {article}
}
@article{griese2017submillimeter,
Author = {F. Griese, T. Knopp, R. Werner, A. Schlaefer, and M. Möddel},
Title = {Submillimeter-Accurate Marker Localization within Low Gradient Magnetic Particle Imaging Tomograms.},
Journal = {International Journal on Magnetic Particle Imaging.},
Year = {(2017).},
Volume = {3.},
Number = {(1),},
Note = {article, fiducial, openaccess},
Url = {https://journal.iwmpi.org/index.php/iwmpi/article/view/103},
Abstract = {Magnetic Particle Imaging (MPI) achieves a high temporal resolution, which opens up a wide range of real-time medical applications such as device tracking and navigation. These applications usually rely on automated techniques for finding and localizing devices and fiducial markers in medical images. In this work, we show that submillimeter-accurate automatic marker localization from low gradient MPI tomograms with a spatial resolution of several millimeters is possible. Markers are initially identified within the tomograms by a thresholding-based segmentation algorithm. Subsequently, their positions are accurately determined by calculating the center of mass of the gray values inside the pre-segmented regions. A series of phantom measurements taken at full temporal resolution (46 Hz) is used to analyze statistical and systematical errors and to discuss the performance and stability of the automatic submillimeter-accurate marker localization algorithm. }
}
@article{Schmiester2017,
Author = {L. Schmiester, M. Möddel, W. Erb, and T. Knopp},
Title = {Direct Image Reconstruction of Lissajous Type Magnetic Particle Imaging Data using Chebyshev-based Matrix Compression.},
Journal = {IEEE Transactions on Computational Imaging.},
Year = {(2017).},
Note = {article, matrix compression, real-time},
Doi = {10.1109/TCI.2017.2706058},
Abstract = {mage reconstruction in magnetic particle imaging (MPI) is done using an algebraic approach for Lissajous-type measurement sequences. By solving a large linear system of equations, the spatial distribution of magnetic nanoparticles can be determined. Despite the use of iterative solvers that converge rapidly, the size of the MPI system matrix leads to reconstruction times that are typically much longer than the actual data acquisition time. For this reason, matrix compression techniques have been introduced that transform the MPI system matrix into a sparse domain and then utilize this sparsity for accelerated reconstruction. Within this work, we investigate the Chebyshev transformation for matrix compression and show that it can provide better reconstruction results for high compression rates than the commonly applied Cosine transformation. By reducing the number of coefficients per matrix row to one, it is even possible to derive a direct reconstruction method that obviates the usage of iterative solvers.}
}
@article{knopp2017review,
Author = {T. Knopp, N. Gdaniec and M. Möddel},
Title = {Magnetic Particle Imaging: From Proof of Principle to Preclinical Applications.},
Journal = {Physics in Medicine & Biology.},
Year = {(2017).},
Volume = {62.},
Number = {(14),},
Pages = {R124},
Note = {article},
Doi = {10.1088/1361-6560/aa6c99},
Abstract = {Tomographic imaging has become a mandatory tool for the diagnosis of a majority of diseases in clinical routine. Since each method has its pros and cons, a variety of them is regularly used in clinics to satisfy all application needs. Magnetic particle imaging (MPI) is a relatively new tomographic imaging technique that images magnetic nanoparticles with a high spatiotemporal resolution in a quantitative way, and in turn is highly suited for vascular and targeted imaging. MPI was introduced in 2005 and now enters the preclinical research phase, where medical researchers get access to this new technology and exploit its potential under physiological conditions. Within this paper, we review the development of MPI since its introduction in 2005. Besides an in-depth description of the basic principles, we provide detailed discussions on imaging sequences, reconstruction algorithms, scanner instrumentation and potential medical applications.}
}
@COMMENT{Bibtex file generated on 2026-5-13 with typo3 si_bibtex plugin. Data from https://www.tuhh.de/ibi/people/martin-moeddel }