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Cvetković, M. & Poljak, D., Electromagneticthermal dosimetry comparison of the homogeneous adult and child brain models based on the SIE approach. Journal of Electromagnetic Waves and Applications, 29(17), pp. 2365–2379, 2015. [Crossref]
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Cvetković, M., Poljak, D., Rogić Vidaković, M. & Ðogaš, Z., TMS induced fields in different brain models. Journal of Electromagnetic Waves and Applications, 30(14), pp. 1820–1835, 2016. [Crossref]
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Open Access
Research article

Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application

M. Cvetković,
D. Poljak
University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Croatia
International Journal of Computational Methods and Experimental Measurements
|
Volume 6, Issue 6, 2018
|
Pages 1182-1191
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

The paper revisits the use of a surface equivalence theorem in deriving the surface integral equation (SIE) based formulation for a homogeneous bio-electromagnetics problem. The vector analog of Green’s 2nd identity is used to obtain the expression for the electric field representing the mathematical foundation of the equivalence theorem. The particular emphasis is put on the treatment of boundary integral when the observation and source points, respectively, coincide. The boundary conditions at infinity are taken into account via the Sommerfeld radiation conditions. The derived coupled SIE set can be used in problems involving biological body exposed to electromagnetic field radiation.

Keywords: Computational electromagnetics, Equivalence principle, Human exposure to electromagnetic fields, Surface integral equation
References
1.
Hand, J., Modelling the interaction of electromagnetic fields (10 MHz– 10 GHz) with the human body: methods and applications. Physics in Medicine and Biology, 53(16), pp. R243–R286, 2008. [Crossref]
2.
Poljak, D., Cavka, D., Dodig, H., Peratta, C. & Peratta, A., On the use of the bound-ary element analysis in bioelectromagnetics. Engineering Analysis with Boundary Elements, 49, pp. 2–14, 2014. [Crossref]
3.
Poljak, D., Human Exposure to Electromagnetic Fields. WIT Press, Boston, 2003.
4.
Cvetković, M. & Poljak, D., An efficient integral equation based dosimetry model of the human brain. Proceedings of EMC EUROPE 2014, Gothenburg, Sweden, 1–4 September 2014, pp. 375–380, 2014.
5.
Poljak, D., Cvetković, M., Peratta, A., Peratta, C., Dodig, H. & Hirata, A., On some integral approaches in EM dosimetry. BIOEM 2016, 2016.
6.
Poggio, A.J. & Miller, E.K., Integral equation solutions of three– dimensional scatter-ing problems. Computer Techniques for Electromagnetics, 2.E., ed. R. Mittra, pp. 159–264, 1987.
7.
Chew, W.C., Tong, M.S. & Hu, B., Integral Equation Methods for Electromagnetic and Elastic Waves. Morgan & Claypol Publishers, San Rafael, CA, 2009.
8.
Cvetković, M., Poljak, D. & Haueisen, J., Analysis of transcranial magnetic stimulation based on the SIE formulation. IEEE Transactions on Biomedical Engineering, 62(6), pp. 1535–1545, 2015. [Crossref]
9.
Wei, F. & Yilmaz, A., A more scalable and Efficient parallelization of the adaptive integral method – Part II: BIOEM Application. IEEE Transactions on Antennas and Propagation, 62(2), pp. 727–738, 2014. [Crossref]
10.
Stratton, J.A. & Chu, L.J., Diffraction theory of electromagnetic waves. Physical Review, 56(1), pp. 99–107, 1939. [Crossref]
11.
Chen, K.M., A mathematical formulation of the equivalence principle. IEEE Transac-tions on Microwave Theory and Techniques, 37(10), pp. 1576–1581, 1989. [Crossref]
12.
Cvetković, M. & Poljak, D., Electromagneticthermal dosimetry comparison of the homogeneous adult and child brain models based on the SIE approach. Journal of Electromagnetic Waves and Applications, 29(17), pp. 2365–2379, 2015. [Crossref]
13.
Cvetković, M., Poljak, D., Rogić Vidaković, M. & Ðogaš, Z., TMS induced fields in different brain models. Journal of Electromagnetic Waves and Applications, 30(14), pp. 1820–1835, 2016. [Crossref]
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Cvetković, M. & Poljak, D. (2018). Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application. Int. J. Comput. Methods Exp. Meas., 6(6), 1182-1191. https://doi.org/10.2495/CMEM-V6-N6-1182-1191
M. Cvetković and D. Poljak, "Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application," Int. J. Comput. Methods Exp. Meas., vol. 6, no. 6, pp. 1182-1191, 2018. https://doi.org/10.2495/CMEM-V6-N6-1182-1191
@research-article{Cvetković2018EquivalencePA,
title={Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application},
author={M. Cvetković and D. Poljak},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2018},
page={1182-1191},
doi={https://doi.org/10.2495/CMEM-V6-N6-1182-1191}
}
M. Cvetković, et al. "Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application." International Journal of Computational Methods and Experimental Measurements, v 6, pp 1182-1191. doi: https://doi.org/10.2495/CMEM-V6-N6-1182-1191
M. Cvetković and D. Poljak. "Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application." International Journal of Computational Methods and Experimental Measurements, 6, (2018): 1182-1191. doi: https://doi.org/10.2495/CMEM-V6-N6-1182-1191
CVETKOVIĆ M， POLJAK D. Equivalence Principle and Surface Integral Equation (Sie) Revisited for Bioelectromagnetics Application[J]. International Journal of Computational Methods and Experimental Measurements， 2018， 6(6)： 1182-1191. https://doi.org/10.2495/CMEM-V6-N6-1182-1191