Hartmut Brauer

Influence of tissue resistivities on neuromagnetic fields and electric potentials studied with a finite element model of the head

Modeling in magnetoencephalography (MEG) and electroencephalography (EEG) requires knowledge of the in vivo tissue resistivities of the head. The aim of this paper is to examine the influence of tissue resistivity changes on the neuromagnetic field and the electric scalp potential. A high-resolution finite element method (FEM) model (452162 elements, 2-mm resolution) of the human head with 13 different tissue types is employed for this purpose. Our main finding was that the magnetic fields are sensitive to changes in the tissue resistivity in the vicinity of the source. In comparison, the electric surface potentials are sensitive to changes in the tissue resistivity in the vicinity of the source and in the vicinity of the position of the electrodes. The magnitude (strength) of magnetic fields and electric surface potentials is strongly influenced by tissue resistivity changes, while the topography is not as strongly influenced. Therefore, an accurate modeling of magnetic field and electric potential strength requires accurate knowledge of tissue resistivities, while for source localization procedures this knowledge might not be a necessity.

Der Einfluß der Randelementediskretisierung auf die Vorwärtsrechnung und das inverse Problem in Elektroencephalographie und Magnetoencephalographie - The Influence of Boundary Element Discretization on the Forward and Inverse Problem in Electroencephalography and Magnetoencephalography

Die Volumenleitermodellierung für die Quellenlokalisierung in der Elektroencephalographie (EEG) und der Magnetoencephalographie (MEG) basiert zunehmend auf der Randelementemethode (boundary element method, BEM). Es wird der Einfluß der Randelementediskretisierung in Abhängigkeit von Dipoltiefe, betrachteter Gehirnregion und quasisphärischer Korrektur auf die Genauigkeit der Lösung der Vorwärtsrechnung und des inversen Problems in MEG und EEG quantifiziert. Dabei werden insbesondere Standardwerte für die generelle Benutzung von BEMModellen für MEG/EEG-Quellenlokalisierung abgeleitet. Dazu werden Simulationen mit Einzeldipolen und Quellenrekonstruktionen aus somatosensorisch evozierten Potentialen und Magnetfeldern benutzt. Es wurde gefunden, daß sich sowohl die globale als auch die lokale Diskretisierung auf die Quellenrekonstruktion auswirkt. Erst bei einer Dreiecksseitenlänge von <10 mm wurden stabile Ergebnisse in MEG und EEG erzielt. Um hinreichend geringe Fehler in diesem stabilen Bereich zu erhalten, darf das Verhältnis von Dipoltiefe zu Dreiecksseitenlänge 0,5 für lineare Randelementeansätze nicht unterschreiten. Die Ergebnisse aus dem Vergleich der Gehirnregionen deuten darauf hin, daß die Ähnlichkeit zur Kugelgeometrie sehr wohl einen Einfluß auf den lokalisierten Dipolort hat, jedoch weniger Einfluß auf die bestimmte Dipolstärke. Die Quellenrekonstruktion unter Verwendung der quasisphärischen Korrektur zeigte sich insgesamt am stabilsten, insbesondere auch bei grober BEM-Diskretisierung.

Reconstruction of extended current sources in a human body phantom applying biomagnetic measuring techniques

We have prepared a human body phantom for experimental verification of inverse solution techniques which are applied to magnetic (and electric) measuring data. Physical models of extended primary current sources were used to generate these fields. Magnetic field maps closed to the phantom surface were recorded by means of multi-channel biomagnetic measuring systems. Different deterministic optimization techniques were applied to both measured and simulated data to reconstruct the impressed current density distribution. We have found that all common used minimum norm methods (L/sub p/-norms, 1/spl les/p/spl les/2) cannot reconstruct the extension of current source distributions satisfactorily. The physical phantom was found to be a suitable tool for validation of source reconstruction techniques.

Source localization in an inhomogeneous physical thorax phantom.

The influence of lung inhomogeneities on focal source localizations in electrocardiography (ECG) and magnetocardiography (MCG) is investigated. A realistically shaped physical thorax phantom with cylindrical lung inhomogeneities is used for electric and magnetic measurements. The lungs are modelled with a special ionic exchange membrane which allows different conductivity compartments without influencing the free ionic current flow. The dipolar current sources are composed of platinum wire and located at different depths and directions between the lung inhomogeneities. We localized the current dipoles with different boundary element method (BEM) models, based on electrical data and simultaneous electrical and magnetic data. Our results indicate the possibility of superadditive information gain by combining electrical and magnetic data for source reconstructions. We found a significant influence of the inhomogeneities on both the calculated source location and the calculated source strength. Mislocalizations of up to 16 mm and wrong dipole strengths of up to 52% were obtained when the lung inhomogeneities were not taken into account for source localization. Dipoles parallel to the lungs showed a larger localization error in depth than dipoles perpendicular to the lungs. We conclude that the incorporation of lung inhomogeneities will improve source localization accuracy in ECG and MCG.

Lorentz force sigmometry: A contactless method for electrical conductivity measurements

The present communication reports a new technique for the contactless measurement of the specific electrical conductivity of a solid body or an electrically conducting fluid. We term the technique “Lorentz force sigmometry” where the neologism “sigmometry” is derived from the Greek letter sigma, often used to denote the electrical conductivity. Lorentz force sigmometry (LoFoS) is based on similar principles as the traditional eddy current testing but allows a larger penetration depth and is less sensitive to variations in the distance between the sensor and the sample. We formulate the theory of LoFoS and compute the calibration function which is necessary for determining the unknown electrical conductivity from measurements of the Lorentz force. We conduct a series of experiments which demonstrate that the measured Lorentz forces are in excellent agreement with the numerical predictions. Applying this technique to an aluminum sample with a known electrical conductivity of rAl ¼ 20:4MS=m and to a copper sample with rCu ¼ 57:92MS=m we obtain rAl ¼ 21:59MS=m and rCu ¼ 60:08MS=m, respectively. This demonstrates that LoFoS is a convenient and accurate technique that may find application in process control and thermo-physical property measurements for solid and liquid conductors. V C 2012 American Institute of Physics.

The influence of conductivity changes in boundary element compartments on the forward and inverse problem in electroencephalography and magnetoencephalography.

Source localization based on magnetoencephalographic and electroencephalographic data requires knowledge of the conductivity values of the head. The aim of this paper is to examine the influence of compartment conductivity changes on the neuromagnetic field and the electric scalp potential for the widely used three compartment boundary element models. Both the analysis of measurement data and the simulations with dipoles distributed in the brain produced two significant results. First, we found the electric potentials to be approximately one order of magnitude more sensitive to conductivity changes than the magnetic fields. This was valid for the field and potential topology (and hence dipole localization), and for the amplitude (and hence dipole strength). Second, changes in brain compartment conductivity yield the lowest change in the electric potentials topology (and hence dipole localization), but a very strong change in the amplitude (and hence in the dipole strength). We conclude that for the magnetic fields the influence of compartment conductivity changes is not important in terms of dipole localization and strength estimation. For the electric potentials however, both dipole localization and strength estimation are significantly influenced by the compartment conductivity.

Fast Computation Technique of Forces Acting on Moving Permanent Magnet

Relative movement of permanent magnet and conductor evokes forces acting on both objects (Lorentz forces). These forces can be used for studying material characteristics of the conducting object (nondestructive testing). The paper compares various modeling techniques (transient, quasi-static, fast-quasi-static) of a moving permanent magnet above conducting plate using 2-D and 3-D finite-element method (FEM). The proposed approaches are applied to calculations of force profiles which enable to identify defects in conductor. The comparison of simulations with measurements performed on a long aluminum bar is also presented.

Finite Element Analysis of Nondestructive Testing Eddy Current Problems With Moving Parts

We present the logical expressions (LE) approach that allows fast computation of three-dimensional eddy current problems, including parts in motion. The approach applies time-dependent logical expressions to describe moving parts of the model on a fixed computational grid. The study is motivated by a novel nondestructive testing technique called Lorentz force eddy current testing (LET), which enables the detection of defects lying deep inside a conducting material. Depending on the definition of the frame of reference, we present two different implementations of the LE approach referred to as 1) moving magnet approach, and 2) moving defect approach. In order to demonstrate the advantages of the LE approach, we compare its results with the sliding mesh technique. The validation of the obtained results with experiments is also presented.

Dependence of the inverse solution accuracy in magnetocardiography on the boundary-element discretization

Modeling in magnetocardiography is increasingly based on the boundary-element method. We quantify the influence of the boundary-element discretization on the cardiomagnetic forward and inverse problem for different dipole depths and regions of the heart. Simulations using single current dipoles and a high resolution boundary-element model (edge length <10 mm) are used to assess models of various complexity (with and without blood masses) and discretization. It is found that the maximum localization error of about 5 mm occurs if the test dipole is very close to one of the boundaries (lungs). Edge lengths of 20, 15, and 8 mm for the torso, lungs, and ventricles, respectively, are sufficient to reach a localization accuracy of 2 mm.

Fast Technique for Lorentz Force Calculations in Non-Destructive Testing Applications

The primary aim of this paper is to present new 2-D/3-D numerical technique providing fast calculations of Lorentz forces acting on a permanent magnet moving relatively to a solid electrically conducting object. This specific field configuration represents a typical problem arising in novel non-destructive testing and evaluation technique known as the Lorentz force eddy-current testing (LET). The proposed technique, referred to as the weak reaction approach (WRA) is based on several model simplifications, which, in the limits of low magnetic Reynolds numbers, allow considerable reduction of the simulation time while maintaining the accuracy of the solution. For evaluation of the computational requirements and verification of the obtained results, the well-established sliding mesh technique is used. Finally, the presented WRA is applied to various parametric studies in form of defect imaging, which can throw light on possible reconstruction and localization of defects by solving an inverse LET problem.