The usefulness of the Laplacian in principal component analysis and dipole source localization

SummaryEvoked potentials are difficult to analyze because multiple sources are active simultaneously. Principal component analysis and dipole localization are two techniques that have been used to disentangle overlapping sources. Both of these techniques have problems. Principal component analysis suffers from a rotation ambiguity. Dipole localization suffers from biases when the model used to derive the sources from the scalp potentials is misspecified. Using computer simulations we demonstrate that by applying both of these techniques to the Laplacian of the voltages rather than to the raw voltages the problems associated with the two techniques are reduced. Computer programs for the analyses are presented in an Appendix.

[1]  S. Cooper.  Chapter 6. , 1887, Interviews with Rudolph A Marcus on Electron Transfer Reactions.

[2]  J. Fermaglich.  Electric Fields of the Brain: The Neurophysics of EEG , 1982 .

[3]  J. P. Ary,et al.  Location of Sources of Evoked Scalp Potentials: Corrections for Skull and Scalp Thicknesses , 1981, IEEE Transactions on Biomedical Engineering.

[4]  Don L. Jewett,et al.  Insidious errors in dipole parameters due to shell model misspecification using multiple time-points , 2005, Brain Topography.

[5]  J. P. Ary,et al.  Spatio-temporal visually evoked scalp potentials in response to partial-field patterned stimulation. , 1980, Electroencephalography and clinical neurophysiology.

[6]  The 2dim-Laplacian field is not suitable to localize sources of EEG activity , 1992, Vision Research.

[7]  R. Verleger,et al.  Principal component analysis of event-related potentials: a note on misallocation of variance. , 1986, Electroencephalography and clinical neurophysiology.

[8]  Richard Srebro.  The laplacian of the scalp potential field: Physical interpretation and practical utility , 1992, Vision Research.

[9]  H. Spekreijse,et al.  Principal components analysis for source localization of VEPs in man , 1987, Vision Research.

[10]  M Scherg,et al.  A new interpretation of the generators of BAEP waves I-V: results of a spatio-temporal dipole model. , 1985, Electroencephalography and clinical neurophysiology.

[11]  A. Achim,et al.  Methods for separating temporally overlapping sources of neuroelectric data , 2005, Brain Topography.

[12]  Don L. Jewett,et al.  Model misspecification detection by means of Multiple Generator Errors, using the observed potential map , 2005, Brain Topography.

[13]  D H Fender,et al.  The dimensionality of the human visual evoked scalp potential. , 1976, Electroencephalography and clinical neurophysiology.

[14]  S. Mulaik,et al.  Foundations of Factor Analysis , 1975 .

[15]  Paul L. Nunez,et al.  The surface laplacian, high resolution EEG and controversies , 2005, Brain Topography.

[16]  R E Ideker,et al.  Eccentric dipole in a spherical medium: generalized expression for surface potentials. , 1973, IEEE transactions on bio-medical engineering.

[17]  Don L. Jewett,et al.  DSL and MUSIC Under model misspecification and noise-conditions , 2005, Brain Topography.

[18]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[19]  S. Klein.  Inverting a Laplacian topography map , 2005, Brain Topography.

[20]  D L Jewett,et al.  Insidious errors in dipole localization parameters at a single time-point due to model misspecification of number of shells. , 1993, Electroencephalography and clinical neurophysiology.

[21]  P. Nunez,et al.  High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces , 1993, IEEE Transactions on Biomedical Engineering.

[22]  William H. Press,et al.  The Art of Scientific Computing Second Edition , 1998 .

[23]  S. Klein,et al.  The topography of visual evoked response properties across the visual field. , 1994, Electroencephalography and clinical neurophysiology.

[24]  C C Wood,et al.  Principal component analysis of event-related potentials: simulation studies demonstrate misallocation of variance across components. , 1984, Electroencephalography and clinical neurophysiology.