arXiv subjects

Martin Möddel

Publications and source records attributed to Martin Möddel.

At least 19 recordsLinked to original sources

arXiv2026

Parameter Estimation for Model-Based Sensing of Magneto-Mechanical Resonators

Magneto-mechanical resonators (MMRs) represent a recently proposed type of passive sensor that enables the estimation of its pose as well as sensing other parameters in its environment. The working principle of MMRs entails an excitation of the sensors by oscillating magnetic fields, followed by a readout process facilitated by inductive receiver coils. The sensing technology relies on real-time parameter estimation. This encompasses the solution of a nonlinear inverse problem, with the induced signals and a suitable forward model as inputs. The aim of this paper is twofold: first, to introduce a reference model and simplified models for the MMR dynamics and inductive readout, and second, to provide robust and real-time capable methods to estimate the model parameters. The effectiveness of the presented methods is evaluated in terms of their real-time potential, precision, and accuracy. All presented methods demonstrate the capacity to estimate the measured signal, with the simplified methods reducing the corresponding parameter estimation time by up to two orders of magnitude at the expense of less than 4 % deviation for large maximum deflection angles.

physics.app-ph↗

arXiv2025

Natural Frequency Dependency of Magneto-Mechanical Resonators on Magnet Distance

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 (MMR), 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. Thereby, the quantity is coupled to the torsional oscillation frequency, e.g. by varying the magnet distance. In this paper, we analyze the (deflection angle-independent) natural frequency dependency 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.

physics.app-ph↗

arXiv2025

Simulating Gadolinium-Induced Magnetic Field Variations for Temperature Sensing with Magneto-Mechanical Resonators

Small-size magneto-mechanical resonators (MMR) represent an emerging class of passive, wireless sensors that combine a sensing functionality with a tracking option. The operation principle is based on a resonating rotor oscillation whose frequency is defined by the magnetic flux density of a stator magnet. One general sensing mechanism is the coupling of an external parameter to this resonator frequency. In this study, we investigate an approach for encoding a temperature information as a shift in the natural oscillation frequency utilizing the temperature-dependent magnetic properties of gadolinium (Gd). We perform an isolated simulation study on the temperature scaling of the magnetic field generation for stators coated with Gd of varying thickness. Our results show that the magnetic phase transition of Gd at its Curie temperature leads to a pronounced change in the magnetic permeability enabling a significant magnetic shielding behavior only for lower temperatures. In the transition regime, we find a peak sensitivity reaching 45.8 Hz/K exceeding existing values from the literature by up to a factor of $\sim$ 20. The findings of this work are an important step toward quantitative high-sensitivity temperature extraction with MMRs.

physics.app-ph↗

arXiv2025

Uncertainties of a Spherical Magnetic Field Camera

Spherical harmonic expansions are well-established tools for estimating magnetic fields from surface measurements and are widely used in applications such as tomographic imaging, geomagnetism, and biomagnetism. Although the mathematical foundations of these expansions are well understood, the impact of real-world imperfections, on the uncertainty of the field model has received little attention. In this work, we present a systematic uncertainty propagation analysis for a magnetic field camera that estimates the field from surface measurements using a spherical array of Hall magnetometers arranged in a spherical t-design. A Monte Carlo-based approach is employed to quantify how sensor-related uncertainties, such as calibration errors and positioning inaccuracies, affect the spatial distribution of the estimated field's uncertainty. The results offer insights into the robustness of spherical harmonic methods and help identify the dominant sources of uncertainty in practical implementations.

physics.ins-det↗

arXiv2025

Real-Time 3D Magnetic Field Camera for a Spherical Volume

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 the development of a magnetometer array designed to measure magnetic fields within a spherical volume at a frame rate of 10 Hz. The array consists of 3D 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 to sequential methods. This work details the design, calibration, and measurement methods of the array. To evaluate its performance, we compare it to a sequential single-sensor measurement by examining a magnetic gradient field. The obtained measurement uncertainties of approx. 1% show the applicability for a variety of applications.

physics.app-ph↗

arXiv2025

Wireless and passive pressure detection using magneto-mechanical resonances in process engineering

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 $0.06~\text{Hz mbar}^{-1}$ and are in agreement with theoretical calculations and measurements. The maximum sensor readout frequency is $2~\text{Hz}$ 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.

physics.app-ph↗

arXiv2024

Resonant Inductive Coupling Network for Human-Sized Magnetic Particle Imaging

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 inductive coupling network is used. Our primary objectives are to achieve floating potentials to ensure patient safety, 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 of 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 to method-of-moment based simulations.

eess.SP↗

arXiv2023

System Characterization of a Human-Sized 3D Real-Time Magnetic Particle Imaging Scanner for Cerebral Applications

Since the initial patent in 2001, the Magnetic Particle Imaging (MPI) community has been striving to develop an MPI scanner suitable for human applications. Numerous contributions from different research fields, regarding tracer development, reconstruction methods, hardware engineering, and sequence design have been employed in pursuit of this objective. In this work, we introduce and thoroughly characterize an improved head-sized MPI scanner with an emphasis on human safety. The scanner is operated by open-source software that enables scanning, monitoring, analysis, and reconstruction, designed to be handled by end users. Our primary focus is to present all technical components of the scanner, with the ultimate objective to investigate brain perfusion imaging in phantom experiments. We have successfully achieved full 3D single- and multi-contrast imaging capabilities at a frame rate of 4 Hz with sufficient sensitivity and resolution for brain applications. To assess system characterization, we devised sensitivity, resolution, perfusion, and multi-contrast experiments, as well as field measurements and sequence analysis. The acquired images were captured using a clinically approved tracer and suitable magnetic field strengths, while adhering to the established human peripheral nerve stimulation thresholds. This advanced scanner holds potential as a tomographic imager for diagnosing conditions such as ischemic stroke or intracranial hemorrhage in environments lacking electromagnetic shielding. Furthermore, due to its low power consumption it may have the potential to facilitate long-term monitoring within intensive care units for various applications.

physics.med-ph↗

arXiv2023

Saline bolus for negative contrast perfusion imaging in magnetic particle imaging

Objective. Magnetic Particle Imaging (MPI) is capable of high temporal resolution measurements of the spatial distribution of magnetic nanoparticles and therefore well suited for perfusion imaging, which is an important tool in medical diagnosis. Perfusion imaging in MPI usually requires a fresh bolus of tracer material to capture the key signal dynamics. Here, we propose a method to decouple the imaging sequence from the injection of additional tracer material, without further increasing the administered iron dose in the body with each image. Approach. A bolus of physiological saline solution without any particles (negative contrast) diminishes the steady-state concentration of a long-circulating tracer during passage. This depression in the measured concentration contributes to the required contrast dynamics. The presence of a long-circulating tracer is therefore a prerequisite to obtain the negative contrast. 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. Every acquired perfusion image thus requires a new bolus of tracer with a sufficiently large iron dose to be visible above the background. Main results. Perfusion parameters are calculated based on the time response of the proposed 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. Significance. Our method opens up the possibility to increase the total monitoring time, while minimizing the iron dose per acquired image.

physics.med-ph↗

arXiv2023

Unique Compact Representation of Magnetic Fields using Truncated Solid Harmonic Expansions

Precise knowledge of magnetic fields is crucial in many medical imaging applications like magnetic resonance imaging or magnetic particle imaging (MPI) as they are the foundation of these imaging systems. For the investigation of the influence of field imperfections on imaging, a compact and unique representation of the magnetic fields using real solid spherical harmonics, which can be obtained by measuring a few points of the magnetic field only, is of great assistance. In this manuscript, we review real solid harmonic expansions as a general solution of Laplace's equation including an efficient calculation of their coefficients using spherical t-designs. We also provide a method to shift the reference point of an expansion by calculating the coefficients of the shifted expansion from the initial ones. These methods are used to obtain the magnetic fields of an MPI system. Here, the field-free-point of the spatial encoding field serves as unique expansion point. Lastly, we quantify the severity of the distortions of the static and dynamic fields in MPI by analyzing the expansion coefficients.

physics.med-ph↗

arXiv2022

Simultaneous Imaging of Widely Differing Particle Concentrations in MPI: Problem Statement and Algorithmic Proposal for Improvement

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.

physics.med-ph↗

arXiv2022

Generalized MPI Multi-Patch Reconstruction using Clusters of similar System Matrices

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.

physics.med-ph↗

arXiv2022

Suppression of Motion Artifacts Caused by Temporally Recurring Tracer Distributions in Multi-Patch Magnetic Particle Imaging

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.

physics.med-ph↗

arXiv2021

Efficient Joint Estimation of Tracer Distribution and Background Signals in Magnetic Particle Imaging using a Dictionary Approach

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 and allows for precise estimation of the background even when the latter is drifting non-linearly over time. 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.

eess.IV↗

arXiv2021

Modeling the Magnetization Dynamics for Large Ensembles of Immobilized Magnetic Nanoparticles in Multi-dimensional Magnetic Particle Imaging

Magnetic nanoparticles (MNPs) play an important role in biomedical applications including imaging modalities such as 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. 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. Thus, the voltage-to-image mapping 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 during immobilization, one can encode the angle of the easy axis into the magnetization response providing a sophisticated benchmark system for model-based approaches. In this work, we address the modeling problem for immobilized, 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 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.

cond-mat.mes-hall↗

arXiv2020

MDF: Magnetic Particle Imaging Data Format

Magnetic particle imaging (MPI) is a tomographic method to determine the spatio-temporal distribution of magnetic nanoparticles. In this document, a file format for the standardized storage of MPI and magnetic particle spectroscopy (MPS) data is introduced. The aim of the Magnetic Particle Imaging Data Format (MDF) is to provide a coherent way of exchanging MPI and MPS data acquired with different devices worldwide. The focus of the MDF is on sequence parameters, measurement data, calibration data, and reconstruction data. The format is based on the hierarchical document format in version 5 (HDF5). This document discusses the MDF version 2.1.0, which is not backward compatible with version 1.x.y.

physics.med-ph↗

arXiv2019

Bimodal intravascular volumetric imaging combining OCT and MPI

Intravascular optical coherence tomography (IVOCT) is a catheter based image modality allowing for high resolution imaging of vessels. It is based on a fast sequential acquisition of A-scans with an axial spatial resolution in the range of 5 to 10 μm, i.e., one order of magnitude higher than in conventional methods like intravascular ultrasound or computed tomography angiography. However, position and orientation of the catheter in patient coordinates cannot be obtained from the IVOCT measurements alone. Hence, the pose of the catheter needs to be established to correctly reconstruct the three-dimensional vessel shape. Magnetic particle imaging (MPI) is a three-dimensional tomographic, tracer-based and radiation-free image modality providing high temporal resolution with unlimited penetration depth. Volumetric MPI images are angiographic and hence suitable to complement IVOCT as a co-modality. We study simultaneous bimodal IVOCT MPI imaging with the goal of estimating the IVOCT pullback path based on the 3D MPI data. We present a setup to study and evaluate simultaneous IVOCT and MPI image acquisition of differently shaped vessel phantoms. First, the infuence of the MPI tracer concentration on the optical properties required for IVOCT is analyzed. Second, using a concentration allowing for simultaneous imaging, IVOCT and MPI image data is acquired sequentially and simultaneously. Third, the luminal centerline is established from the MPI image volumes and used to estimate the catheter pullback trajectory for IVOCT image reconstruction. The image volumes are compared to the known shape of the phantoms. We were able to identify a suitable MPI tracer concentration of 2.5 mmol/L with negligible influence on the IVOCT signal. The pullback trajectory estimated from MPI agrees well with the centerline of the phantoms. (...)

physics.med-ph↗

arXiv2018

Moving Table Magnetic Particle Imaging: A stepwise approach preserving high spatio-temporal resolution

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 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 field of view is usually a few cubic centimeters. To bypass this limitation, additional focus fields and/or external object movements can be applied. In this work, the latter approach is investigated. An object is moved through the scanner bore one step at a time, while the MPI scanner continuously acquires data from its static field of view. Using a 3D phantom and dynamic 3D 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.

physics.med-ph↗