B. Petkovic

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.

Optimal Magnetic Sensor Vests for Cardiac Source Imaging

Magnetocardiography (MCG) non-invasively provides functional information about the heart. New room-temperature magnetic field sensors, specifically magnetoresistive and optically pumped magnetometers, have reached sensitivities in the ultra-low range of cardiac fields while allowing for free placement around the human torso. Our aim is to optimize positions and orientations of such magnetic sensors in a vest-like arrangement for robust reconstruction of the electric current distributions in the heart. We optimized a set of 32 sensors on the surface of a torso model with respect to a 13-dipole cardiac source model under noise-free conditions. The reconstruction robustness was estimated by the condition of the lead field matrix. Optimization improved the condition of the lead field matrix by approximately two orders of magnitude compared to a regular array at the front of the torso. Optimized setups exhibited distributions of sensors over the whole torso with denser sampling above the heart at the front and back of the torso. Sensors close to the heart were arranged predominantly tangential to the body surface. The optimized sensor setup could facilitate the definition of a standard for sensor placement in MCG and the development of a wearable MCG vest for clinical diagnostics.

Computation of Lorentz Force and 3-D Eddy Current Distribution in Translatory Moving Conductors in the Field of a Permanent Magnet

Determination of the 3-D eddy current distribution inside a translatory moving conductor under a permanent magnet can accurately be done by using finite-element method (FEM). However, FEM calculations are very expensive, as they require discretization of the whole conductor volume. In this paper, we propose a new technique, to be called boundary element source method (BESM), where only boundary layers are discretized. The BESM is a modification of the hybrid boundary element method (HBEM). In the BESM, the concentrated point sources placed at the centers of boundary elements for the HBEM are replaced by distributed charge density over the area of the boundary element. This is especially useful in the regions, where neighboring boundary meshes significantly affect one another and when calculation point of eddy current is very close or belong to the surface of a boundary element. The method can handle arbitrary geometries of the specimen as well as the defect and arbitrary orientation of the magnetization vector. The accuracy of the proposed method is verified by comparing the results with the solutions obtained from a finite-element model. The proposed BESM approach is shown to be simple, robust, and computationally accurate.

Calculation of eddy currents in moving conductors using the meshfree charge simulation method

In this paper, the mesh free charge simulation method is used for determination of eddy currents inside a conductor translatory moving in a field of the permanent magnet. Using a reference finite element solution, we investigate the position of the inflated boundary surface where the fictitious sources are randomly located. The method can handle arbitrary shaped conductors and arbitrary oriented magnetization vectors. The proposed procedure is shown to be simple and computationally accurate.

Lorentz force evaluation with an extended area approach

A goal function scan based on an extended area approach is applied to determine size and depth of a defect in Lorentz force evaluation (LFE). Four datasets of a laminated aluminium specimen with a cylindrical defect at depths of 2, 4, 8 and 14 mm are simulated with the finite element method. LFE yields the correct defect sizes and depths for all four defects with a root mean square error of 0.95, 1.21, 1.57 and 4.41 %, respectively.

Lorentz force distribution inside a conductor moving in the vicinity of a magnetic dipole with arbitrary orientation

We report a numerical, integral-free method, to be called Boundary Element Source Method (BESM), for obtaining the electromagnetic force distribution inside a conducting specimen moving in the field of a permanent magnet. The method is computationally advantageous compared to domain methods because only boundary surfaces need to be discretized. Verification is done against a finite element solution. Our initial results show promising performance for further applications in case of more complex magnet and conductor geometries.

Optimizing a magnetic sensor vest for cardiac source imaging

S. Lau 1,2,4 , B. Petkovic 1 , L. Di Rienzo 3 , J. Haueisen 1 , 1 Institute of Biomedical Engineering and Informatics, Ilmenau Technical University, Ilmenau, Germany, 2 Biomagnetic Center, Department of Neurology, University Hospital Jena, Jena, Germany, 3 Politecnico di Milano, Dipartimento di Elettrotecnica, Milano, Italy, 4 Neuroengineering Lab., Dept. of Electrical and Electronic Eng., University of Melbourne, Parkville, Australia, Email: jens.haueisen@tu-ilmenau.de