Medical & Biological Engineering & Computing

, Volume 32, Issue 1, pp 35–42 | Cite as

Interpreting magnetic fields of the brain: minimum norm estimates

  • M. S. Hämäläinen
  • R. J. Ilmoniemi
Biomedical Engineering


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.


Inverse problem Minimum-norm estimate Neuromagnetism 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Ahlfors, S. P., Ilmoniemi, R. J., andHämäläinen, M. S. (1992): ‘Estimates of visually evoked cortical currents,’Electroenceph. Clin. Neurophysiol.,82, pp. 225–236CrossRefGoogle Scholar
  2. 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. 16–20Google Scholar
  3. 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. 587–590Google Scholar
  4. Crowley, C. W., Greenblatt, R. E., andKhalil, I. (1989): ‘Minimum norm estimation of current distributions in realistic geometrics’, —Ibid., in pp. 603–606Google Scholar
  5. Cuffin, B. N., andCohen, D. (1977): ‘Magnetic fields of a dipole in special volume conductor shapes,’IEEE Trans.,BME-24, pp. 372–381Google Scholar
  6. Dallas, W. J. (1985): ‘Fourier space solution to the magnetostatic imaging problems,’Appl. Opt.,24, pp. 4543–4546Google Scholar
  7. 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. 83–87Google Scholar
  8. Golub, G., Heath, M., andWahba, C. (1979): ‘Generalized cross-validation as a method for choosing a good ridge parameter,’Technometrics,21, pp. 215–223CrossRefMathSciNetzbMATHGoogle Scholar
  9. 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 TechnologyGoogle Scholar
  10. 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. 639–644Google Scholar
  11. 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. 413–497CrossRefGoogle Scholar
  12. 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. 793–796Google Scholar
  13. 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. 278–282Google Scholar
  14. Ioannides, A., Bolton, J. andClarke, C. (1990): ‘Continuous probabilistic solutions to the biomagnetic inverse problem,’Inverse Probl. Google Scholar
  15. Jeffs, B., Leahy, R., andSingh, M. (1987): ‘An evaluation of methods for neuromagnetic image reconstruction,’IEEE Trans.,BME-34, pp. 713–723Google Scholar
  16. 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. 673–676Google Scholar
  17. 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. 571–574Google Scholar
  18. 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.Google Scholar
  19. McLain, D. H. (1974): ‘Drawing contours from arbitrary data points,’Comput. J.,17, pp. 318–324Google Scholar
  20. Nenonen, J., Hämäläinen, M., andIlmoniemi, R. (1994): ‘Minimum-norm estimation in a boundary element torso model,’Med. & Biol. Eng. & Comput., 1994,32, (1) 43–49Google Scholar
  21. Plonsey, R. (1969): ‘Bioelectric phenomena’ (McGraw-Hill, New York) p. 212Google Scholar
  22. Sarvas, J. (1987): ‘Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,’Phys. Med. Biol.,32, pp. 11–22CrossRefGoogle Scholar
  23. Singh, M., Doria, D., Henderson, V. W. Huth, G. C., andBeatty, J. (1984): ‘Reconstruction of images from neuromagnetic fields’IEEE Trans.,NS-31, pp. 585–589Google Scholar
  24. 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. 658–667CrossRefGoogle Scholar
  25. 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. 101–139Google Scholar
  26. Williamson, S. J., andKaufman, L. (1981):‘Biomagnetism,’J. Magn. Magn. Mat.,22, pp. 129–201CrossRefGoogle Scholar

Copyright information

© IFMBE 1994

Authors and Affiliations

  • M. S. Hämäläinen
    • 1
  • R. J. Ilmoniemi
    • 1
  1. 1.Low Temperature LaboratoryHelsinki University of TechnologyEspooFinland

Personalised recommendations