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Spatial Filter Approach for Comparison of the Forward and Inverse Problems of Electroencephalography and Magnetoencephalography

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Abstract

We present an analysis of the relative information content of cortical current source reconstructions from electroencephalogram (EEG) and magnetoencephalogram (MEG) forward calculations by examining the spatial filters that relate the internal sources with the externally measured electric potentials and magnetic fields. The forward spatial filters are seen to be low-pass functions of spatial frequency and spatial resolution degrades in external measurements. Inverse spatial filters may be used to reconstruct cortical sources from external data, but since they are high-pass functions of spatial frequency, they must be regularized to avoid instabilities caused by noise at higher spatial frequencies. The regularization process limits the spatial resolution of source reconstructions. EEG forward spatial filters fall off at lower spatial frequencies than MEG filters; hence, there is less information available in higher spatial frequencies resulting in lower spatial resolution in inverse reconstructions. The tangential component of the magnetic field provides even higher spatial resolution than can be obtained using the radial component. An accompanying article examines the surface Laplacian for both the EEG and the MEG. © 2001 Biomedical Engineering Society.

PAC01: 8710+e, 0230Zz, 8719Nn

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REFERENCES

  1. Arthur, R. M. and D. B. Geselowitz. Effect of inhomogeneities on the apparent location and magnitude of a cardiac current dipole source. IEEE Trans. Biomed. Eng. 17:141–146, 1970.

    Google Scholar 

  2. Babiloni, F., C. Babiloni, L. Fattorini, F. Carducci, P. Onorati, and A. Urbano. Performances of surface Laplacian estimators: A study of simulated and real scalp potential distributions. Brain Topogr. 8:35–45, 1995.

    Google Scholar 

  3. Barry, W. H., W. H. Fairbank, D. C. Harrison, K. L. Lehrman, J. A. V. Malmivuo, and J. P. Wikswo, Jr. Measurement of the human magnetic heart vector. Science 198:1159–1162, 1977.

    Google Scholar 

  4. Baumgartner, C. MEG, EEG, and ECoC: Discussion. Acta Neurol. Scand. Suppl. 152:91–92, 1994.

    Google Scholar 

  5. Born, M., and E. Wolf. Principles of Optics. New York: Pergamon, 1975.

    Google Scholar 

  6. Bradshaw, L. A. Measurement and Modeling of Gastrointestinal Bioelectric and Biomagnetic Fields. PhD Dissertation, Vanderbilt University, 1995.

  7. Bradshaw, L. A., and J. P. Wikswo, Jr. A spatial filter approach for evaluation of the surface Laplacian of EEG and MEG. Ann. Biomed. Eng. 29:202–213, 2001.

    Google Scholar 

  8. Bradshaw, L. A., S. H. Allos, J. P. Wikswo, Jr., and W. O. Richards. Correlation and comparison of magnetic and electric detection of small intestinal electrical activity. Am. J. Physiol. 272:G1159–G1167, 1997.

    Google Scholar 

  9. Brenner, D., J. Lipton, L. Kaufman, and S. J. Williamson. Somatically evoked magnetic fields of the human brain. Science 199:81–83, 1978.

    Google Scholar 

  10. Clark, J. and R. Plonsey. The extracellular potential field of the single active nerve fiber in a volume conductor. Biophys. J. 8:842–864, 1968.

    Google Scholar 

  11. Cohen, D., B. N. Cuffin, K. Yunokuchi, R. Maniewski, C. Purcell, G. R. Cosgrove, J. Ives, and J. G. Kennedy. MEG versus EEG localization test using implanted sources in the human brain. Ann. Neurol. 28:811–817, 1990.

    Google Scholar 

  12. Cohen, D. and B. N. Cuffin. Demonstration of useful differences between magnetoencephalogram and electroencephalogram. Electroencephalogr. Clin. Neurophysiol. 56:38–51, 1983.

    Google Scholar 

  13. Cuffin, B. N. and D. Cohen. Comparison of the magnetoencephalogram and electroencephalogram. Electroencephalogr. Clin. Neurophysiol. 47:132–146, 1979.

    PubMed  Google Scholar 

  14. Dallas, W. J. Fourier space solution to the magnetostatic imaging problem. Appl. Opt. 24:4543–4546, 1985.

    Google Scholar 

  15. Ganapathy, N., and J. W. Clark. Extracellular potentials from skeletal muscle. Math. Biosci. 83:61–96, 1987.

    Google Scholar 

  16. Gencer, N. G., S. J. Williamson, A. Gueziec, and R. Hummel. Optimal reference electrode selection for electric source imaging. Electroencephalogr. Clin. Neurophysiol. 99:163–173, 1996.

    Google Scholar 

  17. Geselowitz, D. B. On bioelectric potentials in an inhomogeneous volume conductor. Biophys. J. 7:1–11, 1967.

    Google Scholar 

  18. Geselowitz, D. B. On the magnetic field generated outside an inhomogeneous volume conductor by internal current sources. IEEE Trans. Magn. 6:346–347, 1970.

    Google Scholar 

  19. Gielen, F. L. H., B. J. Roth, and J. P. Wikswo, Jr. Capabilities of a toroid-amplifier system for magnetic measurement of current in biological tissue. IEEE Trans. Biomed. Eng. 33:910–921, 1986.

    Google Scholar 

  20. Hämäläinen, M. S., 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.

    Google Scholar 

  21. Hämäläinen, M. S., and R. J. Ilmoniemi. Interpreting measured magnetic fields of the brain: Estimates of current distributions. (Helsinki University of Technology, Finland), Technical Report No. TKK-F-A559, 1984.

  22. Hämäläinen, M. S. and J. Sarvas. Realistic conductivity geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans. Biomed. Eng. 36:165–171, 1989.

    Google Scholar 

  23. Hari, R., M. Hämäläinen, R. Ilmoniemi, and O. V. Lounasmaa. MEG versus EEG localization test. Letter to the Editor. Ann. Neurol. 30:222–223, 1991.

    Google Scholar 

  24. Jackson, J. D. Classical Electrodynamics. New York: Wiley, 1975.

    Google Scholar 

  25. Kandori, A., K. Tsukada, T. Haruta, Y. Noda, Y. Terada, T. Mitsui, and K. Sekihara. Reconstruction of two-dimensional current distribution from tangential MCG measurement. Phys. Med. Biol. 41:1705–1716, 1996.

    Google Scholar 

  26. Kuc, R. Magnetometer spacing criterion for biomagnetic source imaging. IEEE Trans. Biomed. Eng. 43:1125–1127, 1996.

    Google Scholar 

  27. Kullmann, W. and W. J. Dallas. Fourier imaging of electrical currents in the human brain from their magnetic fields. IEEE Trans. Biomed. Eng. 34:837–842, 1987.

    Google Scholar 

  28. Law, S. K., P. L. Nunez, and R. S. Wijesinghe. Highresolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces. IEEE Trans. Biomed. Eng. 40:145–153, 1993.

    Google Scholar 

  29. Le, J., and A. Gevins. Method to reduce blur distortion from EEGs using a realistic head model. IEEE Trans. Biomed. Eng. 40:517–527, 1993.

    Google Scholar 

  30. Le, J., V. Menon, and A. S. Gevins. Local estimate of surface Laplacian derivation on a realistically shaped scalp surface and its performance on noisy data. Electroencephalogr. Clin. Neurophysiol. 92:433–441, 1994.

    Google Scholar 

  31. Lutkenhoner, B. A simulation study of the resolving power of the biomagnetic inverse problem. Clin. Phys. Physiol. Meas. 12:73–78, 1991.

    Google Scholar 

  32. Malmivuo, J., V. Suihko, and H. Eskola. Sensitivity distributions of EEG and MEG measurements. IEEE Trans. Biomed. Eng. 44:196–208, 1997.

    Google Scholar 

  33. Mosher, J. C., M. E. Spencer, R. M. Leahy, and P. S. Lewis. Error bounds for EEG and MEG dipole source localization. Electroencephalogr. Clin. Neurophysiol. 86:303–321, 1993.

    Google Scholar 

  34. Murro, A. M., J. R. Smith, D. W. King, and Y. D. Park. Precision of dipole localization in a spherical volume conductor: A comparison of referential EEG, magnetoencephalography, and scalp current density methods. Brain Topogr. 8:119–125, 1995.

    Google Scholar 

  35. Nousiainen, J., O. S. Oja, and J. Malmivuo. Normal vector magnetocardiogram. I. Correlation with the normal vector ECG. J. Electrocardiol. 27:221–231, 1994.

    Google Scholar 

  36. Nunez, P. L., and K. L. Pilgreen. The spline Laplacian in clinical neurophysiology: A method to improve EEG spatial resolution. J. Clin. Neurophysiol. 8:397–413, 1991.

    Google Scholar 

  37. Okada, Y. C. Neurogenesis of evoked magnetic fields. In: Biomagnetism: An Interdisciplinary Approach, edited by S. J. Williamson, G.-L. Romani, L. Kaufman, and I. Modena. New York: Plenum, 1982, pp. 399–408.

    Google Scholar 

  38. Pascual-Marqui, R. D., and R. Biscay-Lirio. Spatial resolution of neuronal generators based on EEG and MEG measurements. Int. J. Neurosci. 68:93–105, 1993.

    Google Scholar 

  39. Proakis, J. G., and D. G. Manolakis. Introduction to Digital Signal Processing. New York: Macmillan, 1988.

    Google Scholar 

  40. Rall, W. Branching dendritic trees and motoneuron membrane resistivity. Exp. Neurol. 1:491–527, 1959.

    Google Scholar 

  41. Rosen, A. and G. T. Inouye. A study of the vector magnetocardiographic wave form. IEEE Trans. Biomed. Eng. 22:167–174, 1975.

    Google Scholar 

  42. Roth, B. J., N. G. Sepulveda, and J. P. Wikswo, Jr. Using a magnetometer to image a two-dimensional current distribution. J. Appl. Phys. 65:361–372, 1989.

    Google Scholar 

  43. Roth, B. J., and J. P. Wikswo, Jr. The electrical potential and the magnetic field of an axon in a nerve bundle. Math. Biosci. 76:37–57, 1985.

    Google Scholar 

  44. Rush, S., and D. A. Driscoll. EEG electrode sensitivity—An application of reciprocity. IEEE Trans. Biomed. Eng. 16:15–22, 1969.

    Google Scholar 

  45. Sarvas, J. Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. Phys. Med. Biol. 32:11–22, 1987.

    Article  PubMed  Google Scholar 

  46. Singh, M., R. R. Brechner, and V. W. Henderson. Neuromagnetic localization using magnetic resonance images. IEEE Trans. Biomed. Eng. 11:129–134, 1992.

    Google Scholar 

  47. Srinivasan, R., P. L. Nunez, and R. B. Silberstein. Spatial filtering and neocortical dynamics: Estimates of EEG coherence. IEEE Trans. Biomed. Eng. 45:814–826, 1998.

    Google Scholar 

  48. Stampfli, R. In: Demyelinating Disease, Basic Clinical Electrophysiology, edited by S. G. Waxman and J. M. Ritchie. New York: Raven, 1981.

    Google Scholar 

  49. Tan, S., B. J. Roth, and J. P. Wikswo, Jr. The magnetic field of cortical current sources: The application of a spatial filtering model to the forward and inverse problems. Electroencephalogr. Clin. Neurophysiol. 76:73–85, 1990.

    Google Scholar 

  50. Wijesinghe, R. S. A mathematical model for calculating the vector magnetic field of a single muscle fiber. Math. Biosci. 103:245–274, 1991.

    Google Scholar 

  51. Wikswo, Jr. J. P., High-resolution magnetic imaging: Cellular action currents and other applications. In: NATO ASI on SQUID Sensors: Fundamentals, Fabrication and Applications, edited by H. Weinstock. Dordrecht: Kluwer (in press).

  52. Wikswo, Jr., J. P., A. S. Gevins, and S. J. Williamson. The future of the EEG and MEG. Electroencephalogr. Clin. Neurophysiol. 87:1–9, 1993.

    Google Scholar 

  53. Wikswo, Jr., J. P., and B. J. Roth. Magnetic determination of the spatial extent of a single cortical current source: A theoretical analysis. Electroencephalogr. Clin. Neurophysiol. 69:266–276, 1988.

    Google Scholar 

  54. Williamson, S. J. MEG versus EEG localization test. Letter to the Editor. Ann. Neurol. 30:222, 1991.

    Google Scholar 

  55. Wood, C. C., D. Cohen, B. N. Cuffin, M. Yarita, and T. Allison. Electrical sources in human somatosensory cortex: Identification by combined magnetic and and potential recordings. Science 227:1051–1053, 1985.

    Google Scholar 

  56. Woosley, J. K., B. J. Roth, and J. P. Wikswo, Jr. The magnetic field of a single axon: A volume conductor model. Math. Biosci. 76:1–36, 1985.

    Google Scholar 

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Authors and Affiliations

  1. Living State Physics Group, Department of Physics and Astronomy, Vanderbilt University, Nashville, TN

    L. A. Bradshaw & J. P. Wikswo Jr.

  2. Department of Physics and Engineering Science, Lipscomb University, Nashville, TN

    L. A. Bradshaw

  3. Brain Physics Group, Department of Biomedical Engineering, Tulane University, New Orleans, LA

    R. S. Wijesinghe

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  1. L. A. Bradshaw
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  2. R. S. Wijesinghe
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  3. J. P. Wikswo Jr.
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Bradshaw, L.A., Wijesinghe, R.S. & Wikswo, J.P. Spatial Filter Approach for Comparison of the Forward and Inverse Problems of Electroencephalography and Magnetoencephalography. Annals of Biomedical Engineering 29, 214–226 (2001). https://doi.org/10.1114/1.1352641

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