# Magnetoencephalography Inverse Problem for Spherical and Spheroid Models

- 5 Downloads

Magnetoencephalography produces big data. The processing of these data in order to reconstruct signal sources with a given accuracy is an extremely ill-posed problem. The main purpose of this work is an extension of our previous results to spheroid model providing a more accurate solution. In certain models of a human head (spherical and spheroid), the Biot–Savart law and IC analysis give a background for the detailed investigation in order to develop an algorithm for primary motor cortex localization. For a general case of the spheroid model, it is possible to approximately solve the inverse problem, neglecting volume magnetic field near the points of maxima of the magnetic field and taking into account only primary magnetic field. This paper presents a stepwise algorithm to obtain MEG inverse problem solution under the assumptions of discreteness of signal sources, originating from distinct functional brain areas and superficial location of the signal sources.

## Preview

Unable to display preview. Download preview PDF.

## References

- 1.S. Baillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,”
*IEEE Sig. Process. Mag.*,**18**, No. 6, 14–30 (2001).CrossRefGoogle Scholar - 2.J. Sarvas, “Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,”
*Phys. Med. Biol.*,**32**, 11–22 (1987).CrossRefGoogle Scholar - 3.K. Friston, L. Harrison, J. Daunizeau, S. Kiebel, C. Phillips, N. Trujillo-Barreto, R. Henson, G. Flandin, and J. Mattoutf, “Multiple sparse priors for the M/EEG inverse problem,”
*Neuro Image*,**39**, 1104–1120 (2008).Google Scholar - 4.T. V. Zakharova, S. Yu. Nikiforov, M. B. Goncharenko, M. A. Dranitsyna, G. A. Klimov, M. S. Khaziakhmetov, and N. V. Chayanov, “Signal processing methods for the localization of nonrenewable brain regions,”
*Syst. Mean. Inform.*,**22**, No. 2, 157–176 (2012).Google Scholar - 5.M. S. Khaziakhmetov and T. V. Zakharova, “Algorithms for myogram reference points search with the aim of irrecoverable brain regions localization,”
*Stat. Methods Estim. Hypoth. Test.*,**25**, 56–63 (2013).Google Scholar - 6.T. V. Zakharova, M. B. Goncharenko, and S. Yu. Nikiforov, “Inverse problem solving method based on clustering of brain surface,”
*Stat. Methods Estim. Hypoth. Test.*,**25**, 120–125 (2013).Google Scholar - 7.V. Ye. Bening, A.K. Gorshenin, and V.Yu. Korolev, “Asymptotically optimum hypothesis test for number of components in mixture of probability distribution,”
*Inform. Appl.*,**5**, No. 3, 4–16 (2011).Google Scholar - 8.V. M. Allakhverdieva, E. V. Chshenyavskaya, M. A. Dranitsyna, P. I. Karpov, and T.V. Zakharova, “Approach for inverse problem solving, assuming gamma distribution of myogram noise within rest intervals and utilizing independent component analysis,”
*J. Math. Sci.*, to appear (2018).Google Scholar - 9.R. Uitert, D. Weinstein, and C. Johnson, “Can a spherical model substitute for a realistic head model in forward and inverse MEG simulations?” in:
*Proc. 13th Int. Conf. on Biomagnetism*, Jena, Germany (2002), pp. 798–800.Google Scholar - 10.L.D. Landau, L.P. Pitaevskii, and E.M. Lifshitz,
*Electrodynamics of Continuous Media*, Pergamon, New York (1984).Google Scholar - 11.M. Hamalainen, 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.*,**65**, 413–497 (1993).CrossRefGoogle Scholar - 12.B. Cuffin and D. Cohen, “Magnetic fields of a dipole in special volume conductor shapes,”
*IEEE Trans. Biomed. Eng.*,**24**, 372–381 (1977).CrossRefGoogle Scholar - 13.A. Hyvarinen, J. Karhunen, and E. Oja,
*Independent Component Analysis*, Wiley, New-York (2001).Google Scholar - 14.V. E. Bening, M. A. Dranitsyna, T. V. Zakharova, and P. I. Karpov, “Independent component analysis for inverse problem in multidipole model magnetoencephalogram sources,”
*Inform. Appl.*,**8**, No. 2, 79–87 (2014).Google Scholar - 15.R. J. Ilmoniemi, M. S. Hamalainen, and J. Knuutila, “The forward and inverse problems in the spherical model,” in:
*Biomagnetism: Applications and Theory*, H. Weinberg, G. Stroink, and T. Katila (eds.), Pergamon, New York (1985), pp. 278–282.Google Scholar - 16.G. Dassios, “The magnetic polential for the ellipsoidal MEG problem,”
*J. Comput. Math.*,**25**, 145–156 (2007).MathSciNetGoogle Scholar - 17.J. C. de Munck, “The potential distribution in a layered anisotropic spheroidal volume conductor,”
*J. Appl. Phys.*,**64**, 464–470 (1988).CrossRefGoogle Scholar - 18.M. Dranitsyna, T. Zakharova, V. Allakhverdiyeva, and E. Chshenyavskaya, “Probability density function of myogram noise and its role in localization of brain activity,” in:
*XXXII International Seminar on Stability Problems for Stochastic Models*, Trondheim, Norway (2014), pp. 25–26.Google Scholar