Development and application of a new method for field computation in biomedical engineering
Final Report Abstract
We have introduced a new numerical method for the determination of propagation of volume currents produced by sources in the brain and in the heart and simulated the distribution of the electric scalar potential at a number of locations on the head and torso surface. The method is based on accumulation of charges on boundary layers which occur wherever there is a non‐zero component of the electric field parallel to the gradient of conductivity. In this way, we have established a theoretical foundation for electoencephalography (EEG) and electrocardiography (ECG) recordings that does not require numerical integration and can be implemented in a very simple way. The EEG and ECG signals are comprehensively compared against reference boundary element and finite element solutions, respectively, through topography and magnitude errors. Additionally, a distribution of the electric field intensity inside an one‐layer sphere used as the head model during the Transcranial Magnetic Stimulation has been accurately determined. However, calculation of the magnetic field produced by sources in the brain or in the heart did not yet yield satisfactory results. The Boundary element source method has been applied to determine the eddy currents induced in a conductive specimen, translatory moving in the field of a permanent magnet. Based on these currents, we further determined Lorentz forces acting on a magnet due to their interaction with the field of a permanent magnet. These forces are the key component of the novel technique for the characterization of deep lying defects in conductive materials, referred to as Lorentz force evaluation. Our method has some difficulties: first, it shows lack of accuracy when there is a large conductivity difference inside a model, especially in the case of extremely thin layers and, second, close proximity of the source to the boundary layer introduces numerical errors into the forward computation. These difficulties apply particularly to the EEG forward problem and can be partially overcome by an isolated problem approach and a local refinement strategy, respectively. To conclude, the main concern during this project was to build a mathematical model rich enough to provide realistic bioelectromagnetic and Lorentz force signals and simple enough to be easily implemented. In spite of its shortcomings, the proposed approach essentially fulfills these requirements and is therefore a good candidate to address inverse problems. This will be a part of future works.
Publications
- Optimal magnetic sensor vests for cardiac source imaging, Sensors, 16 (2016)
S. Lau, B. Petković and J. Haueisen
(See online at https://doi.org/10.3390/s16060754) - Assessment of two forward solution approaches in Lorentz force evaluation, IEEE Transactions on Magnetics, vol. 54, no. 3, 6200105, 2017
E.‐M. Dölker, R. Schmidt, K. Weise, B. Petković, M. Ziolkowski, H. Brauer, and J. Haueisen
(See online at https://doi.org/10.1109/TMAG.2017.2765347) - Computation of Lorentz force and 3‐D eddy current distribution in translatory moving conductors in the field of a permanent magnet, IEEE Transactions on Magnetics, vol. 53, No. 2, 7000109, 2017
B. Petković, K. Weise and J. Haueisen
(See online at https://doi.org/10.1109/TMAG.2016.2622223) - New EEG forward solution, European medical and biological engineering conference (EMBEC) 2017, June 11‐15, 2017, Tampere, Finland
B. Petković and J. Haueisen
- Scanning method for indoor localization using the RSSI approach, Journal of Sensors and Sensor Systems, vol. 6, pp. 247‐251, 2017
A. Warda, B. Petković and H. Töpfer
(See online at https://doi.org/10.5194/jsss-6-247-2017) - SCSM for Calculation of Motion‐Induced Eddy Currents in Isotropic and Anisotropic Conductive Objects, Transactions on Magnetics, vol. 54, no. 3, 7204804, 2017
M. Ziolkowski, R. Schmidt, B. Petković, S. Gorges, J. M. Otterbach, K. Weise, and H. Brauer
(See online at https://doi.org/10.1109/TMAG.2017.2765505)
