Roland Eichardt

Tabu Search Optimization of Magnetic Sensor Systems for Magnetocardiography

This paper addresses the question of optimal sensor placement for magnetocardiographic field imaging. New magnetic sensor technologies allow less restrictive sensor positioning in this application. We develop a constraint framework for sensor positioning and use tabu search (TS) and particle swarm optimization (PSO) for finding an optimal set of sensors, whereby a new PSO algorithm is designed to fit the needs of our constraint framework. Numerical simulations are carried out with a three compartment boundary element torso model and a multi-dipole heart model. We find an optimal value of about 20 to 30 vectorial sensors and both TS and PSO yield similar sensor distributions. The comparison to sensors on regular grids shows that optimization of vectorial magnetic sensor setups may significantly improve reconstruction quality and that the number of sensors can be reduced.

Tangential and radial epileptic spike activity: Different sensitivity in EEG and MEG

Objective: Observations in epileptic patients show that interictal spikes are sometimes only visible in electroencephalography (EEG) and sometimes only in magnetoencephalography (MEG). This observation cannot readily be explained by the theoretical sensitivities of EEG and MEG based on analytical models. In this context, we aimed to study the directional sensitivity of radial and tangential spike activity in numerical simulations using realistic head models. Methods: We calculated the signal-to-noise ratio (SNR) of simulated spikes at varying orientations and with varying background activity in 12 brain regions in 4 volunteers. Different levels of background activity were modeled by adjusting the amplitudes of several thousand dipoles distributed in the cortex. Results: For a fixed realistic background activity, we found a higher SNR for MEG spikes for spike orientations that deviated not >30° from the tangential direction. In contrast, we found a higher SNR for EEG spikes that deviated not >45° from the radial direction. When the radial background activity was selectively increased, the sensitivity of EEG for radially oriented spikes decreased; when the tangential background activity selectively increased, the sensitivity of MEG for tangentially oriented spikes was decreased. Conclusions: Our simulations provide a possible explanation for the clinically observed differences in epileptic spike detection between EEG and MEG. Epileptic spike detection can be improved by analyzing a combination of EEG and MEG data.

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.

Influence of Sensor Variations on the Condition of the Magnetostatic Linear Inverse Problem

We examine the influence of randomized variations of the sensor directions on the condition of the linear inverse problem in magnetostatics. Sensor arrays with varied sensor directions are compared with arrays using perfectly in parallel aligned sensors. As evaluation criterion the condition number of the related lead field matrix is used. The results reveal that for mono-axial sensor arrays the condition of the linear inverse problem can be considerably improved, when sensors are directed non-uniformly. Furthermore, our findings indicate that also small variations of the sensor Z-positions of planar mono-axial arrays can lead to a better condition.

Reconstruction of Multiple Neuromagnetic Sources Using Augmented Evolution Strategies— A Comparative Study

The localization of dipolar sources in the brain based on electroencephalography (EEG) or magnetoencephalography (MEG) data is a frequent problem in the neurosciences. Deterministic standard approaches such as the Levenberg-Marquardt (LM) method often have problems in finding the global optimum of the associated nonlinear optimization function, when two or more dipoles are to be reconstructed. In such cases, probabilistic approaches turned out to be superior, but their applicability in neuromagnetic source localizations is not yet satisfactory. The objective of this study was to find probabilistic optimization strategies that perform better in such applications. Thus, hybrid and nested evolution strategies (NES) which both realize a combination of global and local search by means of multilevel optimizations were newly designed. The new methods were bench-marked and compared to the established evolution strategies (ES), to fast evolution strategies (FES), and to the deterministic LM method by conducting a two-dipole fit with MEG data sets from neuropsychological experiments. The best results were achieved with NES.

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...

Sensitivity Comparisons of Cylindrical and Hemi-Spherical Coil Setups for Magnetic Induction Tomography

In this simulation study, we evaluate and compare the cylindrical and the hemi-spherical coil setups of two Magnetic Induction Tomography (MIT) systems using sensitivity analysis. Furthermore, different parameters for the size and the number of measurement and excitation coils are tested. For evaluating the sensitivity to conductivity values, the edge finite element method with uniform tetrahedral elements is utilized. The volume of interest is defined by a sphere, which represents a generic measurement object similar to the human head. A figure of merit that describes the general sensitivity to conductivity changes within the upper half of this volume, and two plots representing the distribution of sensitivity values are computed. Our findings indicate that the hemi-spherical MIT system with a smaller distance between the layer of coils and the measurement object shows a clearly higher sensitivity compared to the cylindrical MIT system. In addition, the two simulated setups with larger coil areas provide higher sensitivities in relation to the standard setups, while the difference between the hemi-spherical setups using a different number of coils with identical areas is relatively small.

Magnetic nanoparticle imaging by random and maximum length sequences of inhomogeneous activation fields

Biomedical applications of magnetic nanoparticles require a precise knowledge of their biodistribution. From multi-channel magnetorelaxometry measurements, this distribution can be determined by means of inverse methods. It was recently shown that the combination of sequential inhomogeneous excitation fields in these measurements is favorable regarding the reconstruction accuracy when compared to homogeneous activation . In this paper, approaches for the determination of activation sequences for these measurements are investigated. Therefor, consecutive activation of single coils, random activation patterns and families of m-sequences are examined in computer simulations involving a sample measurement setup and compared with respect to the relative condition number of the system matrix. We obtain that the values of this condition number decrease with larger number of measurement samples for all approaches. Random sequences and m-sequences reveal similar results with a significant reduction of the required number of samples. We conclude that the application of pseudo-random sequences for sequential activation in the magnetorelaxometry imaging of magnetic nanoparticles considerably reduces the number of required sequences while preserving the relevant measurement information.

Comparison of three- and single-shell volume conductor models in magnetoencephalography

M. Stenroos, Department of Biomedical Engineering and Computational Science, Aalto University, Espoo, Finland / MRC Cognition and Brain Sciences Unit, Cambridge, England, matti.stenroos@aalto.fi A. Hunold, Institute of Biomedical Engineering and Informatics, Technical University Ilmenau, Germany, alexander.hunold@tu-ilmenau.de R. Eichardt, Institute of Biomedical Engineering and Informatics, Technical University Ilmenau, Germany, roland.eichardt@tu-ilmenau.de J. Haueisen, Institute of Biomedical Engineering and Informatics, Technical University Ilmenau, Germany, jens.haueisen@tu-ilmenau.de

Adaptive spatial harmonic analysis of EEG data using Laplacian eigenspace

Electroencephalography is an important diagnostic tool for functional investigations of the human brain. Recent EEG measurement technologies provide high numbers of electrodes and sampling rates, which results in a considerable quantity of data. For the analysis of this EEG data, efficient signal analysis and decomposition methods are essential. In this paper a new method for spatial harmonic analysis of EEG data using the Laplacian eigenspace of the meshed surface of electrode positions is presented. The resulting eigenspace enables the spatial harmonic analysis, filtering, denoising and decomposition of EEG data. For a proof of concept, the proposed approach is applied to an 128 channel EEG recording of visual evoked potentials. A set of harmonic spatial basis functions for the EEG electrode setup is estimated. The EEG data are spatially decomposed and low pass filtered using the harmonic spatial basis functions.