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Local Polynomial Estimate of Surface Laplacian

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Abstract

This paper describes a method for estimating the surface Laplacian of brain potentials. The method consists of two steps: local surface approximation by its tangent plane and local polynomial fitting. Compared to previous methods for estimating surface Laplacian, this method has some new features. First, it can estimate the surface Laplacian at any point of the scalp, including the locations of the peripheral electrodes. Secondly, it estimates the brain potential and the surface Laplacian at any point simultaneously. This reduces the risk of error propagation, which occurs when the brain potential is interpolated first and the surface Laplacian is then computed based on the interpolated brain potential. Finally, the method automatically adapts to noisy data by using more or less measurements at neighboring electrodes based on estimated noise level. Simulations suggest that this method is effective. Application to event-related potentials are also presented.

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References

  • Awada, K., Jackson, D., Baumann, S., Williams, J., Wilton, D., Fink, P. and Prasky, B. Effect of conductivity uncertainties and modeling errors on EEG source localization using a 2-D model. IEEE Trans. Biomed. Eng., 1998, 45: 1135-1145.

    Google Scholar 

  • Babiloni, F., Babiloni, C., Carducci, F., Fattorini, L., Anello, C., Onorati, P. and Urbano, A. High resolution EEG: a new model-dependent spatial deblurring method using a realistically-shaped MR-constructed subject's head model. Electroenceph. and Clin. Neurophysiol., 1997, 102: 69-80.

    Google Scholar 

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

    Google Scholar 

  • Babiloni, F., Babiloni, C., Carducci, F., Fattorini, L., Onorati, P. and Urbano, A. Spline Laplacian estimate of EEG potentials over a realistic magnetic resonance-constructed scalp surface model. Electroenceph. and Clin. Neurophysiol., 1996, 98: 363-373.

    Google Scholar 

  • Babiloni, F., Carducci, F., Babiloni, C. and Urbano A. Improved realistic Laplacian estimate of highly-sampled EEG potentials by regularization techniques. Electroenceph. and Clin. Neurophysiol., 1998, 106: 336-343.

    Google Scholar 

  • Biggins, C., Fein, G., Raz, J. and Amir, A. Artifactually high coherences result from using spherical spline computation of scalp current density. Electroenceph. and Clin. Neurophysiol., 1991, 79: 413-419.

    Google Scholar 

  • van Burik, M., Knosche, T., Edlinger, G., Neuper, C., Pfurtscheller, G. and Peters, M. Post-movement beta oscillations studied with linear estimation. Electroenceph. and Clin. Neurophysiol., 1998, 106: 195-198.

    Google Scholar 

  • Edlinger, G., Pfurtscheller, G., Burik, M. and Wach, P. Post-movement EEG synchronization studied with different high resolution methods. Brain Topography, 1997, 10: 103-113.

    Google Scholar 

  • Fan, J., Gasser, T., Gijbels, I., Brockmann, M. and Engel, J. Local polynomial regression: optimal kernels and asymptotic minimax efficiency. Ann. Inst. Statist. Math., 1997, 49: 79-99.

    Google Scholar 

  • Fein, G., Raz, J. and Turetsky, B. Brain electrical activity: the promise of new technologies. In: S. Zakhari and E. Witt (Eds.)., Imaging in Alcohol Research. Proc. of a Workshop on Imaging in Alcohol Research, Wild Dunes, SC, 9–11 May, 1991: 49-78.

  • Fuchs, M., Drenckhahn, R., Wischman, H.-A. and Wagner, M. An improved boundary element model for realistic volume conductor modeling. IEEE Trans. Biomed. Eng., 1998a, 45: 980-997.

    Google Scholar 

  • Fuchs, M., Wagner, M., Wischman, H.-A., Kohler, T. and Theissen, A. Improving source reconstructions by combining bioelectric and biomagnetic data. Electroenceph. and Clin. Neurophysiol., 1998b, 107: 93-111.

    Google Scholar 

  • Gasser, Th. and Müller, H. Estimating regression functions and their derivatives by the kernel method. Scand. J. Statist., 1984, 11: 171-185.

    Google Scholar 

  • Gevins, A. High resolution evoked potentials of cognition. Brain Topography, 1996, 8: 189-199.

    Google Scholar 

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

    Google Scholar 

  • Katznelson, R.D. EEG recording, electrode placement, and aspects of generator localization. Ch. 6 in Electric Fields of The Brain: The Neurophysics of EEG, P.L. Nunez, Oxford University Press, New York, 1981.

    Google Scholar 

  • Koles, Z. Trends in EEG source localization. Electroenceph. and Clin. Neurophysiol., 1998, 106: 127-37.

    Google Scholar 

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

    Google Scholar 

  • Marin, G., Guerin, C., Baillet, S., Garnero, L. and Meunier, G. Influence of skull anisotropy for the forward and inverse problem in EEG: simulation studies using FEM on realistic head model. Human Brain Mapping, 1998, 6: 250-269.

    Google Scholar 

  • Mosher, J. and Leahy, R. Recursive MUSIC: a framework for EEG and MEG source localization. IEEE Trans. Biomed. Eng., 1998, 45: 1342-1354.

    Google Scholar 

  • Nunez, P.L. Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, New York, 1995.

    Google Scholar 

  • Nunez, P.L., Silberstein, R.B., Cadusch, P.J., Wijesinghe, R.S., Westdrop, A.F., and Srinivasan, R. A theoretical and experimental study of high resolution EEG based on surface Laplacians and cortical imaging. Electroenceph. and Clin. Neurophysiol., 1994, 90: 40-57.

    Google Scholar 

  • Oostendrop, T. and Oosterom, A. The surface Laplacian of the potential: theory and application. IEEE Trans. Biomed. Eng., 1996, 43: 394-407.

    Google Scholar 

  • Perrin, F., Bertrand, O. and Pernier, J. Scalp current density mapping: value and estimation from potential data. IEEE Trans. Biomed. Eng., 1987, 34: 283-288.

    Google Scholar 

  • Perrin, F., Pernier, J., Bertrand, O. and Echallier, J.F. Spherical splines for scalp potential and current density mapping. Electroenceph. and Clin. Neurophysiol., 1989, 72: 184-187.

    Google Scholar 

  • Sidman, R., Semel, J., Lagerlund, T. and Ford, M. The effect of reference-electrode choice on the spatial resolution of topographical potential maps in the discrimination of deep cerebral sources. J. Neurosci. Methods, 1996, 68: 175-184.

    Google Scholar 

  • Srinivasan, R., Nunez, P., Tucker, D., Silberstein, R. and Cadusch, P. Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials. Brain Topography, 1996, 8: 355-366.

    Google Scholar 

  • Srinivasan, R., Nunez, P. and Silberstein, R. Spatial filtering and neocortical dynamics: estimation of EEG coherence. IEEE Trans. Biomed. Eng., 1998, 45: 814-826.

    Google Scholar 

  • Tenke, C., Kayser, J., Fong, R., Leite, P., Towey, J. and Bruder, G. Response-and stimulus-related ERP asymmetries in a tonal oddball task: a Laplacian analysis. Brain Topography, 1998, 10: 201-210.

    Google Scholar 

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Authors and Affiliations

  1. Department of Psychiatry, SUNY Health Science Center at Brooklyn, Neurodynamics Laboratory, Brooklyn, NY, USA

    Kongming Wang & Henri Begleiter

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  1. Kongming Wang
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  2. Henri Begleiter
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Wang, K., Begleiter, H. Local Polynomial Estimate of Surface Laplacian. Brain Topogr 12, 19–29 (1999). https://doi.org/10.1023/A:1022225522447

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