volume | PIER Journals

Abstract

In this paper a multisphere particle method is developed to estimate the solution of the Poisson's equation with Neumann boundary conditions describing the neuronal human brain activity. The partial differential equations governing the relationships between neural current sources and the data produced by neuroimaging technique, are able to compute the scalp potential and magnetic field distributions generated by the neural activity. A numerical approach is proposed with current dipoles as current sources and going on in the computation by avoiding the mesh construction. The current dipoles are into an homogeneous spherical domain modeling the head and the computational approach is extended to multilayered configuration with different conductivities. A good agreement of the numerical results is shown compared for the first time with the analytical ones.

1. Hamalainen, M., R. Hari, R. J. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, "Magnetoencephalography --- Theory, instrumentation and applications to noninvasive studies of the working human brain," Rev. Mod. Phys, Vol. 65, 413-497, 1993.
doi:10.1103/RevModPhys.65.413

2. Darvas, F. and D. Pantazis, "Mapping human brain function with MEG and EEG: Methods and validation," Neuroimage, Vol. 23, S289-S299, 2004.
doi:10.1016/j.neuroimage.2004.07.014

3. Plonsey, R., Biomagnetic Phenomena, McGraw-Hill, 1969.

4. Zhang, Z., "A fast method to compute surface potentials generated by dipoles within multilayer anisotropic spheres," Phys. Med. Biol., Vol. 40, 335-349, 1995.
doi:10.1088/0031-9155/40/3/001

5. Bishop, G. H., "Potential phenomena in thalamus and cortex," Electroencephalography and Clinical Neurophysiology, Vol. 1, No. 1-4, 421-436, 1949.

6. Brazier, M. A. B., "A study of the electrical field at the surface of the head," Electroencephalography and Clinical Neurophysiology Supplement, Vol. 2, 38-52, 1949.

7. Sholl, D. A., "The Organization of the Cerebral Cortex," Wiley, 1956.

8. Landau, W. M. and E. Potentials, The Neurosciences --- A Study Program, G. C. Quarton, T. Melnechuk, and F. O. Schmitt, Rockefeller University Press, 1967.

9. De Munck, J. C., B. W. van Dijk, and H. Spekreijse, "Mathematical dipoles are adequate to describe realistic generators of human brain activity," IEEE Trans. Biomed. Eng., Vol. 35, 960-966, 1988.
doi:10.1109/10.8677

10. Sarvas, J., "Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem," Phys. Med. Biol., Vol. 32, 11-22, 1987.
doi:10.1088/0031-9155/32/1/004

11. Schimpf, P. H., C. Ramon, and J. Haueisen, "Dipole models for the EEG and MEG," IEEE Trans. Biomed. Eng., Vol. 49, 409-418, 2002.
doi:10.1109/10.995679

12. Yao, D., "Electric potential produced by a dipole in a homogeneous conducting sphere," IEEE Trans. Biomed. Eng., Vol. 47, 964-966, 2000.

13. Gencer, N. G. and I. O. Tanzer, "Forward problem solution of electromagnetic source imaging using a new BEM formulation with high-order elements," Phys. Med. Biol., Vol. 44, 2275-2287, 1999.
doi:10.1088/0031-9155/44/9/314

14. Tanzer, O., S. Jarvenpaa, J. Nenonen, and E. Somersalo, "Representation of bioelectric current sources using whitney elements in the finite element method," Phys. Med. Biol., Vol. 50, 3023-3039, 2005.
doi:10.1088/0031-9155/50/13/004

15. Haueisen, J., C. Hafner, H. Nowak, and H. Brauer, "Neuromagnetic ¯eld computation using the multiple multipole method," Int. J. Numer. Model., Vol. 9, 145-158, 1996.
doi:10.1002/(SICI)1099-1204(199601)9:1/2<145::AID-JNM233>3.0.CO;2-U

16. Pohl-Alfaro, M., O. Yanez-SuArez, J. R. Jimenez-Alaniz, and V. Medina-Ba~nuelos, "Realistic meshless conductor model for EEG inverse problems," International Journal of Bioelectromagnetism, Vol. 10, 176-189, 2008.

17. Ala, G., E. Francomano, and F. Viola, "A wavelet operator on the interval in solving Maxwell's equations," Progress In Electromagnetic Research Letters,, Vol. 27, 133-140, 2011.
doi:10.2528/PIERL11090505

18. Ala, G., M. L. Di Silvestre, F. Viola, and E. Francomano, "Soil ionization due to high pulse transient currents leaked by earth electrodes," Progress In Electromagnetics Research B, Vol. 14, 1-21, 2009.
doi:10.2528/PIERB09022103

19. Liu, G. R., Mesh Free Methods --- Moving beyond the Finite Element Method, CRC Press, 2003.

20. Gingold, R. A. and J. J. Monaghan, "Smoothed particle hydrodynamics: Theory and application to non-spherical stars," Mon. Not. Roy. Astron. Soc., Vol. 181, 375-389, 1977.

21. Liu, M. B. and G. R. Liu, "Smoothed particle hydrodynamics (SPH): An overview and recent developments," Archives of Computational Methods in Engineering, Vol. 17, 25-76, 2010.
doi:10.1007/s11831-010-9040-7

22. Monaghan , J. J., "An introduction to SPH," Comput. Phys. Commun., Vol. 48, 89-96, 1988.
doi:10.1016/0010-4655(88)90026-4

23. Monaghan, J. J., "Smoothed particle hydrodynamics," Annu. Rev. Astron. Astrophys., Vol. 30, 543-574, 1992.
doi:10.1146/annurev.aa.30.090192.002551

24. Von Ellenrieder, N., C. H. Muravchik, and A. Nehorai, "A meshless method for solving the EEG forward problem," IEEE Trans. Biomed. Eng.,, Vol. 52, 249-257, 2005.
doi:10.1109/TBME.2004.840499

25. Demirel, O., B. Schrader, I. F. Sbalzarini, and , "A parallel particle method for solving the EEG source localization forward problem," Proc. 6th Intl. Symp. Health Informatics and Bioinformatics --- HIBIT, 2011.

26. Ala, G. and E. Francomano, "An improved smoothed particle electromagnetics method in 3D time domain simulations," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields,, Vol. 25, No. 4, 325-337, 2012.
doi:10.1002/jnm.834

27. Ala, G. and E. Francomano, "Smoothed particle electromagnetics modelling on HPC-GRID environment," Applied Computational Electromagnetics Society Journal, Vol. 27, No. 3, 229-237, 2012.

28. Ala, G., G. Di Blasi, and E. Francomano, "A numerical meshless particle method in solving the magnetoencephalography forward problem," International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 25, 428-440, 2012.
doi:10.1002/jnm.1828

29. Ala, G. and E. Francomano, "A marching in time meshless kernel based solver for full-wave electromagnetic simulation," Numerical Algorithms, Springer, 2012, ISSN: 1017-1398, DOI 10.1007/s11075-012-9635-1 .

30. Ala, G., E. Francomano, A. Tortorici, E. Toscano, and F. Viola, "Corrective meshless particle formulations for time domain Maxwell's equations," Journal of Computational and Applied Mathematics, Vol. 210, No. 1, 34-46, 2007.
doi:10.1016/j.cam.2006.10.054

31. Ala, G., E. Francomano, A. Spagnuolo, and A. Tortorici, "A Meshless approach for electromagnetic simulation of metallic carbon nanotubes," Journal of Mathematical Chemistry, Vol. 48, No. 1, 72-77, 2010.
doi:10.1007/s10910-009-9627-0

32. Di Blasi, G., E. Francomano, A. Tortorici, and E. Toscano, "A smoothed particle image reconstruction method," Calcolo, Vol. 48, 61-74, 2011.
doi:10.1007/s10092-010-0028-3

33. Ahonen, A. I., M. S. Hamalainen, M. J. Kajola, J. E. T. Knuutila, P. P. Laine, O. V. Lounasmaa, L. T. Parkkonen, J. T. Simola, and C. D. Tesche, "122-channel squid instrument for investigating the magnetic signals from the human brai," Physica Scripta, Vol. T49A, 198-205, 1993.
doi:10.1088/0031-8949/1993/T49A/033

34. Zhang, Y. and L.Wu, "An MR brain images classifier via principal component analysis and kernel support vector machine," Progress In Electromagnetics Research, Vol. 130, 369-388, 2012.

Professor Guido Ala

Prof. Elisa Francomano