Abstract
The authors have applied estimation theory to the problem of determining primary current distributions from measured neuromagnetic fields. In this procedure, essentially nothing is assumed about the source currents, except that they are spatially restricted to a certain region. Simulation experiments show that the results can describe the structure of the current flow fairly well. By increasing the number of measurements, the estimate can be made more localised. The current distributions may be also used as an interpolation and an extrapolation for the measured field patterns.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Ahlfors, S. P., Ilmoniemi, R. J., andHämäläinen, M. S. (1992): ‘Estimates of visually evoked cortical currents,’Electroenceph. Clin. Neurophysiol.,82, pp. 225–236
Ahonen, A. I., Hämäläinen, M. S., Kajola, M. J., Knuutila, J. E. T., Laine, P. P., Lounasmaa, O. V., Simola, J. T., Tesche, C. D. andVilkman, V. A. (1992): ‘A 122-channel magnetometer covering the whole head’in Dittmar, A. andFroment, J. C. (Eds.): Proc. Satellite Symp. on Neuroscience and Technology, 14th Annual Conf. of the IEEE Engineering in Medicine and Biology Society (IEEE Engineering in Medicine and Biology Society, Lyon) pp. 16–20
Clarke, C. J. S., Ioannides, A. A., andBolton, J. P. R. (1989): ‘Localised and distributed source solutions for the biomagnetic inverse problem I, inWilliamson, S. J., Hoke, M., Stroink, G., andKotani, M. (Eds.), ‘Advances in biomagnetism’ (Plenum, New York) pp. 587–590
Crowley, C. W., Greenblatt, R. E., andKhalil, I. (1989): ‘Minimum norm estimation of current distributions in realistic geometrics’, —Ibid., in pp. 603–606
Cuffin, B. N., andCohen, D. (1977): ‘Magnetic fields of a dipole in special volume conductor shapes,’IEEE Trans.,BME-24, pp. 372–381
Dallas, W. J. (1985): ‘Fourier space solution to the magnetostatic imaging problems,’Appl. Opt.,24, pp. 4543–4546
De Munck, J. C., Hämäläinen, M. S., andPeters, M. J. (1991): ‘The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics’,Clin. Phys. Physiol. Meas.,12(Suppl. A), pp. 83–87
Golub, G., Heath, M., andWahba, C. (1979): ‘Generalized cross-validation as a method for choosing a good ridge parameter,’Technometrics,21, pp. 215–223
Hämäläinen, M. S. andIlmoniemi, R. J. (1984): ‘Interpreting measured magnetic fields of the brain: estimates of current distributions.’ Technical Report TKK-F-A559, Helsinki University of Technology
Hämäläinen, M. S. (1989): ‘A 24-channel planar gradiometer: System design and analysis of neuromagnetic data’in Williamson, S. J., Hoke, M., Stroink, G. andKotani, M. (Eds.): ‘Advances in biomagnetism’ (Plenum, New York) pp. 639–644
Hämäläinen, M. S., Hari, R., Ilmoniemi, R., Knuutila, J., andLounasmaa, O. V. (1993): ‘Magnetoencephalography—theory, instrumentation, and applications to noninvasive studies of the working human brain,’Rev. Mod. Phys.,65, pp. 413–497
Ilmoniemi, R. J., andNumminen, J. K. (1992): ‘Synthetic magnetometer channels for standard representation of data’in Hoke, M., Erné, S. N., Okada, Y. C. andRomani, G. L. (Eds.): ‘Biomagnetism 91: clinical aspects’ (Elsevier, Amsterdam) pp. 793–796
Ilmoniemi, R. J., Hämäläinen, M. S., andKnuutila, J. (1985): ‘The forward and inverse problems in the spherical model’in Weinberg, H., Stroink, G. andKatila, T. (Eds.): ‘Biomagnetism: applications & theory’ (Pergamon Press, New York) pp. 278–282
Ioannides, A., Bolton, J. andClarke, C. (1990): ‘Continuous probabilistic solutions to the biomagnetic inverse problem,’Inverse Probl.
Jeffs, B., Leahy, R., andSingh, M. (1987): ‘An evaluation of methods for neuromagnetic image reconstruction,’IEEE Trans.,BME-34, pp. 713–723
Kajola, M., Ahlfors, S., Ehnholm, G. J., Hällström, J., Hämäläinen, M. S., Ilmoniemi, R. J., Kiriranta, M., Knuutila, J., Lounasmaa, O. V., Tesche, C. D., andVilkman, V. (1989): ‘A 24-channel magnetometer for brain research’in Williamson, S. J., Hoke, M., Stroink, G., andKotani, M. (Eds.): ‘Advances in biomagnetism’ (Plenum, New York) pp. 673–676
Kullmann, W. H., Jandt, K. D., Rehm, K., Schlitt, H. A., Dallas, W. J. andSmith, W. E. (1989): ‘A linear estimation approach to biomagnetic imaging’ —ibid. in pp. 571–574
Malmivuo, J. (1976): ‘On the detection of the magnetic heart vector—an application of the reciprocity theorem’. PhD Thesis, Acta Polytechnica Scandinavica, Electrical Engineering Series 39, Finnish Academy of Technical Sciences, Helsinki.
McLain, D. H. (1974): ‘Drawing contours from arbitrary data points,’Comput. J.,17, pp. 318–324
Nenonen, J., Hämäläinen, M., andIlmoniemi, R. (1994): ‘Minimum-norm estimation in a boundary element torso model,’Med. & Biol. Eng. & Comput., 1994,32, (1) 43–49
Plonsey, R. (1969): ‘Bioelectric phenomena’ (McGraw-Hill, New York) p. 212
Sarvas, J. (1987): ‘Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,’Phys. Med. Biol.,32, pp. 11–22
Singh, M., Doria, D., Henderson, V. W. Huth, G. C., andBeatty, J. (1984): ‘Reconstruction of images from neuromagnetic fields’IEEE Trans.,NS-31, pp. 585–589
Smith, W. E., Dallas, W. J., Kullman, W. H., andSchlitt, H. A. (1990): ‘Linear estimation theory applied to the reconstruction of a 3-D vector current distribution,’Appl. Opt.,29, pp. 658–667
Tripp, J. H. (1983): ‘Physical concepts and mathematical models’in Williamson, S. J., Romani, G.-L., Kaufman, L., andModena, I. (Eds.): ‘Biomagnetism: an interdisciplinary approach’ (Plenum Press, New York) pp. 101–139
Williamson, S. J., andKaufman, L. (1981):‘Biomagnetism,’J. Magn. Magn. Mat.,22, pp. 129–201
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hämäläinen, M.S., Ilmoniemi, R.J. Interpreting magnetic fields of the brain: minimum norm estimates. Med. Biol. Eng. Comput. 32, 35–42 (1994). https://doi.org/10.1007/BF02512476
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02512476