Daniel Baumgarten

Magnetic nanoparticle imaging by means of minimum norm estimates from remanence measurements

In magnetic nanoparticle imaging, magnetic nanoparticles are coated and functionalized to bind to specific targets. After measuring their magnetic relaxation or remanence, their distribution can be determined by means of inverse methods. The reconstruction algorithm presented in this paper includes first a dipole fit using a Levenberg–Marquardt optimizer to determine the reconstruction plane. Secondly, a minimum norm estimate is obtained on a regular grid placed in that plane. Computer simulations involving different parameter sets and conditions show that the used approach allows for the reconstruction of distributed sources, although the reconstructed shapes are distorted by blurring effects. The reconstruction quality depends on the signal-to-noise ratio of the measurements and decreases with larger sensor-source distances and higher grid spacings. In phantom measurements, the magnetic remanence of nanoparticle columns with clinical relevant sizes is determined with two common measurement systems. The reconstructions from these measurements indicate that the approach is applicable for clinical measurements. Our results provide parameter sets for successful application of minimum norm approaches to Magnetic Nanoparticle Imaging.

Advancements in Magnetic Nanoparticle Reconstruction Using Sequential Activation of Excitation Coil Arrays Using Magnetorelaxometry

Magnetic nanoparticles can be employed for a broad range of biomedical applications where the knowledge of the distribution of the magnetic nanoparticles is of importance for efficacy, patients safety, etc. The need exists to have an as accurate as possible quantification of the unknown particles distribution. Magnetorelaxometry (MRX) measurements are able to measure the magnetic induction originating from a certain distribution of magnetically activated nanoparticles. Starting from these measurements it is possible to determine the distribution using a minimum norm estimation technique. This approach is however ill-posed. We sequentially activate the magnetic nanoparticles through the use of excitation coil arrays with the aim to reduce the ill-posedness. This paper presents some advancements in magnetic nanoparticle reconstruction in terms of reconstruction quality using numerical simulations. The results show that inhomogeneous sequential activation is a proper alternative to homogeneous activation with Helmholtz coils since an increase in accuracy with a factor ranging from 1.5 until 2 is obtained. The presented numerical techniques coupled to MRX measurements can be of significant aid so to have more quantitative knowledge of the biodistribution.

A Spatio-Temporal Approach for the Solution of the Inverse Problem in the Reconstruction of Magnetic Nanoparticle Distributions

The estimation of magnetic nanoparticle distributions is essential for their medical application. A possible technique is the reconstruction of these distributions from multichannel magnetorelaxometry measurements. In this paper, a novel minimum norm approach for the solution of this inverse problem based on a spatio-temporal expansion of the generally applied spatial lead field matrix is presented. The performance of this method is quantitatively studied in simulations and compared to the conventional static technique. The influence of the relevant parameters signal-to-noise ratio in the data, time constant of the temporal model, and TSVD regularization parameter is investigated. Our results indicate that the novel spatio-temporal approach significantly improves the reconstruction quality.

Adapting source grid parameters to improve the condition of the magnetostatic linear inverse problem of estimating nanoparticle distributions

The problem of estimating magnetic nanoparticle distributions from magnetorelaxometric measurements is addressed here. The objective of this work was to identify source grid parameters that provide a good condition for the related linear inverse problem. The parameters investigated here were the number of sources, the extension of the source grid, and the source direction. A new measure of the condition, the ratio between the largest and mean singular value of the lead field matrix, is proposed. Our results indicated that the source grids should be larger than the sensor area. The sources and, consequently, the magnetic excitation field, should be directed toward the Z-direction. For underdetermined linear inverse problems, such as in our application, the number of sources affects the condition to a relatively small degree. Overdetermined magnetostatic linear inverse problems, however, benefit from a reduction in the number of sources, which considerably improves the condition. The adapted source grids proposed here were used to estimate the magnetostatic dipole from simulated data; the L2-norm, residual, and distances between the estimated and simulated sources were significantly reduced.

Magnetorelaxometry procedures for quantitative imaging and characterization of magnetic nanoparticles in biomedical applications.

Abstract Background: Quantitative knowledge about the spatial distribution and local environment of magnetic nanoparticles (MNPs) inside an organism is essential for guidance and improvement of biomedical applications such as magnetic hyperthermia and magnetic drug targeting. Magnetorelaxometry (MRX) provides such quantitative information by detecting the magnetic response of MNPs following a fast change in the applied magnetic field. Methods: In this article, we review our MRX based procedures that enable both the characterization and the quantitative imaging of MNPs in a biomedical environment. Results: MRX characterization supported the selection of an MNP system with colloidal stability and suitable cellular MNP uptake. Spatially resolved MRX, a procedure employing multi-channel MRX measurements allowed for in-vivo monitoring of the MNP distribution in a pre-clinical carcinoma animal model. Extending spatially resolved MRX by consecutive magnetization of distinct parts of the sample led to a demonstration of MRX tomography. With this tomography, we reconstructed the three dimensional MNP distribution inside animal sized phantoms with a sensitivity of milligrams of MNPs per cm3. In addition, the targeting efficiency of MNPs in whole blood was assessed using a flow phantom and MRX quantification. Conclusion: These MRX based measurement and analysis procedures have substantially supported the development of MNP based biomedical applications.

Real-Time MEG Source Localization Using Regional Clustering

With its millisecond temporal resolution, Magnetoencephalography (MEG) is well suited for real-time monitoring of brain activity. Real-time feedback allows the adaption of the experiment to the subject’s reaction and increases time efficiency by shortening acquisition and off-line analysis. Two formidable challenges exist in real-time analysis: the low signal-to-noise ratio (SNR) and the limited time available for computations. Since the low SNR reduces the number of distinguishable sources, we propose an approach which downsizes the source space based on a cortical atlas and allows to discern the sources in the presence of noise. Each cortical region is represented by a small set of dipoles, which is obtained by a clustering algorithm. Using this approach, we adapted dynamic statistical parametric mapping for real-time source localization. In terms of point spread and crosstalk between regions the proposed clustering technique performs better than selecting spatially evenly distributed dipoles. We conducted real-time source localization on MEG data from an auditory experiment. The results demonstrate that the proposed real-time method localizes sources reliably in the superior temporal gyrus. We conclude that real-time source estimation based on MEG is a feasible, useful addition to the standard on-line processing methods, and enables feedback based on neural activity during the measurements.

Localisation of buried ferromagnetic objects based on minimum‐norm‐estimations: A simulation study

Purpose – The purpose of this paper is to examine the localisation of ferromagnetic objects buried in the underground. More specifically, it deals with the reconstruction of the XY‐positions, the depths (Z‐positions), the number, and the extension of the objects based on geomagnetic measurements. This paper introduces a minimum‐norm reconstruction approach and evaluates its performance in a simulation study.Design/methodology/approach – A minimum‐L2‐norm estimation based on the truncated singular value decomposition method with lead field weighting is proposed in order to localise geomagnetic sources. The sensor setup and positions are taken from real measurements. The source space is formed by an automatically generated grid. At each grid point, a magneto‐static dipole is assumed.Findings – Sources with different depths and XY‐positions could be successfully reconstructed. The proposed approach is not overly sensitive to errors/noise in measurement values and sensor positions.Originality/value – The appr...

Spatially Resolved Measurement of Magnetic Nanoparticles Using Inhomogeneous Excitation Fields in the Linear Susceptibility Range (<1mT)

For small excitation fields in the microtesla (μT) range, the dependency of the magnetic moment of magnetic iron oxide nanoparticles (MNP) on the external field can be regarded as linear. Sensitive superconducting quantum interference devices (SQUIDs) enable the detection of the response of MNP in biological tissue in the pT range. The co-registration of the excitation field is reduced by appropriate geometrical configuration of excitation coil and sensor coil. MNPs in a wide range of mean diameter and distribution parameters can be used for signal generation. The spatial distribution of MNP is reconstructed using data from a parallel multi-sensor and sequential multi-coil arrangement and applying linear estimation techniques. The time delayed response of MNP due to Brownian and Neel relaxation processes represents a specific signal not being influenced by the diamagnetic contribution of water in the tissue. We present the theoretical background and measurement data from different setups that will exemplify the concept.

A Novel Marker Design for Magnetic Marker Monitoring in the Human Gastrointestinal Tract

Magnetic marker monitoring (MMM) is a technique to determine the motility of the gastrointestinal tract and to observe the dissolution of pharmaceutical compounds. Todays magnetic markers usually consist of magnetized magnetite. Because of their weak magnetic fields, highly sensitive sensor systems are required. For a wider class of applications, stronger markers and more flexible measurement setups are necessary. In this paper, a novel marker design is introduced. This marker comprises one permanent magnet and a compartment of iron powder in a magnetically unstable configuration. During dissolution of the pharmaceuticals, the powder is redistributed around the magnet, thereby altering the externally measured magnetic induction. Based on this design, magnetically marked tablets and capsules were prepared and their magnetic field during dissolution was observed. Magnetic induction values were between 16 and 0.2 μT at distances of 5-30 cm, which is considerably higher compared to the pico-Tesla range of conventional markers. During dissolution, the magnetic induction decreased by between 14% and 27%. These values could be confirmed in detailed finite element method simulations. In conclusion, the present results indicate that our novel marker design is well suited for MMM with more flexible sensor technologies, such as magnetoresistive sensors.

Analysis of Vestibular Labyrinthine Geometry and Variation in the Human Temporal Bone

Stable posture and body movement in humans is dictated by the precise functioning of the ampulla organs in the semi-circular canals. Statistical analysis of the interrelationship between bony and membranous compartments within the semi-circular canals is dependent on the visualization of soft tissue structures. Thirty-one human inner ears were prepared, post-fixed with osmium tetroxide and decalcified for soft tissue contrast enhancement. High resolution X-ray microtomography images at 15 μm voxel-size were manually segmented. This data served as templates for centerline generation and cross-sectional area extraction. Our estimates demonstrate the variability of individual specimens from averaged centerlines of both bony and membranous labyrinth. Centerline lengths and cross-sectional areas along these lines were identified from segmented data. Using centerlines weighted by the inverse squares of the cross-sectional areas, plane angles could be quantified. The fit planes indicate that the bony labyrinth resembles a Cartesian coordinate system more closely than the membranous labyrinth. A widening in the membranous labyrinth of the lateral semi-circular canal was observed in some of the specimens. Likewise, the cross-sectional areas in the perilymphatic spaces of the lateral canal differed from the other canals. For the first time we could precisely describe the geometry of the human membranous labyrinth based on a large sample size. Awareness of the variations in the canal geometry of the membranous and bony labyrinth would be a helpful reference in designing electrodes for future vestibular prosthesis and simulating fluid dynamics more precisely.