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Performances of surface Laplacian estimators: A study of simulated and real scalp potential distributions

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Summary

This paper presents a study of the performance of various local and spherical spline methods currently in use for the surface Laplacian (SL) estimate of scalp potential distributions. The SL was estimated from simulated instantaneous event-related scalp potentials generated over a three-shell spherical head model. Laplacian estimators used planar and spherical scalp models. Noise of increasing magnitude and spatial frequency was added to the potential distributions in order to simulate noise presumed to contaminate scalp-recorded event-related potentials. A comparison of noise effects on various Laplacian estimates was made for increasing number of “electrode” positions in variants of the 10–20 system. Furthermore, to evaluate the error due to the use of unrealistic scalp models, the matching between SL estimates of human scalp-recorded movement-related potentials computed on spherical and realistically-shaped MRI-constructed models of the scalp was examined. With all methods the error of the SL estimate increased proportionally with the magnitude and spatial frequency of noise. Increased number of “electrodes” up to 256 significantly reduced the error (p<0.05). In general, the best SL estimates were computed by second and third order splines including λ correction, the performances of the second order spline being better with more than 64 “electrodes”. Compared with spline Lapladans, the best local methods provided nearly equal estimates with low spatial sampling (19 and 28 “electrodes”), as well as high spatial frequency noise. The error of the SL estimate due to unrealistic scalp model was significant, and it augmented with increased spatial sampling from 64 to 128 electrodes.

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References

  • Babiloni, F., Babiloni, C., Carducci, F., Fattorini, L., Onorati, P. and Urbano, A. Estimate of the surface Laplacian of potential distribution over a realistic model of the scalp. Proceedings of V International Congress of Brain Electromagnetic Topography, Munster (Germany), 1994a: 110.

  • Babiloni, F., Carducci, F., Alfano, B., Frunzio, M., Fattorini, L., Babiloni, C., Onorati, P. and Urbano, A. A new triangulation algorithm for 3D realistic reconstruction of the head from magnetic resonance images in high resolution EEG studies. Proceedings of V International Symposium of Biomedical Engineering, Santiago de Compostela (Spain), 1994b: 228–229.

  • Biggins, C.A., Fein, G., Ratz, J. and Amir, A. Artifactually high coherence results from using spherical spline computation of scalp current density. Electroenceph. clin. Neurophysiol., 1991, 79: 413–419.

    Google Scholar 

  • Biggins, C.A., Ezekiel, F. and Fein, G. Spline computation of scalp current density and coherence: a reply to Perrin. Electroenceph. clin. Neurophysiol., 1992, 83: 172–174.

    Google Scholar 

  • Davila, C.E. and Mobin, M.S. Weighted averaging of evoked potentials. IEEE Trans. Biomed. Eng., 1992, 39: 4, 338–45.

    Google Scholar 

  • Deecke, L., Grozinger, B. and Kornhuber, H. Voluntary finger movement in man: Cerebral potentials and theory. Biol. Cybern., 1976, 23: 99–119.

    Google Scholar 

  • Duchon, J. Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. R. A.I.R.O. Anal. Num., 1976, 10: 5–12.

    Google Scholar 

  • Filligoi, G., Capitanio, L., Babiloni, F., Fattorini, L., Urbano, A. and Cerutti, S. Reduction of ocular artifacts in source current density mappings by ARX2 filtering. Med. Eng. Phys., 1995, 12 (4): 282–290.

    Google Scholar 

  • Gasser, T., Sroka, L. and Mocks, J. The transfer of EOG activity into the EEG for eyes open and closed. Electroenceph. clin. Neurophysiol., 1985, 61: 181–193.

    Google Scholar 

  • Gasser, T., Sroka, L. and Mocks, J. The correction of EOG artefacts by frequency dependent and frequency independent methods. Electroenceph. clin. Neurophysiol., 1986, 23: 704–712.

    Google Scholar 

  • Gevins, A. Dynamic functional topography of cognitive task. Brain Topogr., 1989, 2:37–56.

    Google Scholar 

  • Gevins, A., Brickett, P., Costales, B., Le, J. and Reutter, B. Beyond topographic mapping: towards functional-anatomical imaging with 124-channel EEG and 3-D MRIs. Brain Topogr., 1990, 1: 3–64.

    Google Scholar 

  • Gevins, A., Brickett, P., Reutter, B. and Desmond, J. Seeing through the skull: advanced EEGs use MRIs to accurately measure cortical activity from the scalp. Brain Topogr., 1991, 4: 125–131.

    Google Scholar 

  • Hjorth, B. An on line transformation of EEG scalp potentials into orthogonal source derivations. Electroenceph. clin. Neurophysiol., 1975, 39: 526–530.

    Google Scholar 

  • Koles, Z.J., Kasmia, A., Paranjape, R. and Mc Lean, D.R. Computed radial-current topography of the brain: patterns associated with normal and abnormal EEG. Electroenceph. clin. Neurophysiol., 1989, 72:41–47.

    Google Scholar 

  • Law, S.K., Nunez, P. and Wijesinghe, R.S. High resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces. IEEE Trans. Biomed. Eng., 1993, BME-40:(2) 145–153.

    Google Scholar 

  • Le, J., Vinod, M. and Gevins, A. Local estimate of surface Laplacian derivation on a realistically shaped scalp surface and its performance on noisy data. Electroenceph. clin. Neurophysiol., 1994, 92: 433–441.

    Google Scholar 

  • McKay, D.M. On line source density computation with a minimum of electrodes. Electroenceph. clin. Neurophysiol., 1983, 56:696–698.

    Google Scholar 

  • Mc Kay, D.M.Source analysis of scalp potentials during evaluated action. I Coronal distribution. Exp. Brain Res., 1984, 54: 73–85.

    Google Scholar 

  • Murray, S. Theory and problems of vector analysis and an introduction to tensor analysis. Mc Graw Hill, New York, 1978.

    Google Scholar 

  • Nagamine, T., Kaji, R., Syugo, S., Hamano, T., Shibasaki, H. and Kimura, J. Current source density mapping of somatosensory evoked responses following medial and tibial nerve stimulation. Electroenceph. clin. Neurophysiol., 1992, 84: 248–256.

    Google Scholar 

  • Nunez, P. Electric fields of the brain. Oxford University Press, New York, 1981.

    Google Scholar 

  • Nunez, P. Estimation of large scale neocortical source activity with EEG surface Laplacians. Brain Topogr., 1989, 2: 141–154.

    Google Scholar 

  • Nunez, P. Localization of brain activity with electroencephalography in: Advanced in Neurology, vol. 54: Susumu Sato (Ed.), Magnetoencephalography, Raven Press, New York, 1990.

    Google Scholar 

  • Nunez, P., Pilgreen, K., Westdorp, A., Law, S. and Nelson, A. A visual study of surface potentials and Laplacians due to distributed neocortical sources: computer simulations and evoked potentials. Brain Topogr., 1991, 4: 151–168.

    Google Scholar 

  • Nunez, P.L., Silberstein, R.B., Cadiush, P.J., Wijesinghe, J., Westdorp, A.F. and Srinivasan, R. A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging. Electroenceph. clin. Neurophysiol., 1994, 90:40–57.

    Google Scholar 

  • Oppenheim, P. and Scheffer, B. Digital signal processing, Mc Graw Hill, 1975.

  • Perrin, F., Bertrand, O. and Pernier, J. Scalp current density mapping: value and estimation from potential data. IEEE Trans. Biomed. Eng., 1987, 34: 283–287.

    Google Scholar 

  • Perrin, F., Pernier, J., Bertrand, O. and Echallier, J.F. Spherical spline for potential and current density mapping. Electroenceph. clin. Neurophysiol., 1989, 72: 184–187.

    Google Scholar 

  • Perrin, F., Pernier, J., Bertrand, O. and Echallier, J.F. Corrigendum EEG 02274. Electroenceph. clin. Neurophysiol., 1990, 76: 565.

    Google Scholar 

  • Perrin, F. Comments on article by Biggins et al., Electroenceph. clin. Neurophysiol., 1992, 83: 171–172.

    Google Scholar 

  • Raz, J., Turetsky, B. and Fein, G. Confidence intervals for the signal-to-noise ratio when a signal embedded in noise is observed over repeated trials. IEEE Trans. Biomed. Eng., 1988, 35: 646–649.

    Google Scholar 

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

    Google Scholar 

  • Soufflet, L., Touissant, M., Luthringer, R., Gresser, J., Minot, R. and Macher, J.P. A statistical evaluation of the main interpolation methods applied to 3-dimensional EEG mapping. Electroenceph. clin. Neurophysiol., 1991, 79: 393–402.

    Google Scholar 

  • Tang, Y. and Norcia, A.M. Improved processing of the steadystate evoked potential. Electroenceph. clin. Neurophysiol, 1993, 88:(4) 323–34.

    Google Scholar 

  • Thickbroom, G., Mastaglia, F., Carrol, W. and Davis, H. Source derivation: Application to topographic mapping of visual evoked potentials. Electroenceph. clin. NeurophysioL, 1984, 59: 279–285.

    Google Scholar 

  • Turetsky, B.I., Raz, J. and Fein, G. Noise and signal power and their effects on evoked potential estimation. Electroenceph. clin. NeurophysioL, 1988, 71: 310–318.

    Google Scholar 

  • Turetsky, B.I., Raz, J. and Fein, G. Estimation of trial-to-trial variation in evoked potential signals by smoothing across trials. Psychophysiology, 1989, 26: 700–711.

    Google Scholar 

  • Wahba, G. and Wendelberger, J. Some new mathematical methods for variation objective analysis using splines and cross-validation. Monthly Weather Rev., 1980, 108: 36–57.

    Google Scholar 

  • Zar, H. Biostatistical analysis. Prentice Hall, New York, 1984.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Human Physiology, University of Rome ‘La Sapienza’, 00185, Rome, Italy

    F. Babiloni, C. Babiloni, L. Fattorini, F. Carducci, P. Onorati & A. Urbano (Professor and Director of the Institute of Human Physiology)

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  1. F. Babiloni
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  2. C. Babiloni
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  3. L. Fattorini
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  4. F. Carducci
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  5. P. Onorati
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  6. A. Urbano
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Additional information

The research was supported by a MURST Grant 60% (Facolta', 1992). The authors thank Prof. Paul Nunez for his helpful comments and suggestions. They also thank Oreste Bagni and Roberto Ciuffa for technical assistance, and Dr. Mary Artero for the revision of the English form of the manuscript.

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Babiloni, F., Babiloni, C., Fattorini, L. et al. Performances of surface Laplacian estimators: A study of simulated and real scalp potential distributions. Brain Topogr 8, 35–45 (1995). https://doi.org/10.1007/BF01187668

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