Quantitative analysis of spatial sampling error in the infant and adult electroencephalogram

The purpose of this report was to determine the required number of electrodes to record the infant and adult electroencephalogram (EEG) with a specified amount of spatial sampling error. We first developed mathematical theory that governs the spatial sampling of EEG data distributed on a spherical approximation to the scalp. We then used a concentric sphere model of current flow in the head to simulate realistic EEG data. Quantitative spatial sampling error was calculated for the simulated EEG, with additive measurement noise, for 64, 128, and 256 electrodes equally spaced over the surface of the sphere corresponding to the coverage of the human scalp by commercially available "geodesic" electrode arrays. We found the sampling error for the infant to be larger than that for the adult. For example, a sampling error of less than 10% for the adult was obtained with a 64-electrode array but a 256-electrode array was needed for the infant to achieve the same level of error. With the addition of measurement noise, with power 10 times less than that of the EEG, the sampling error increased to 25% for both the infant and adult, for these numbers of electrodes. These results show that accurate measurement of the spatial properties of the infant EEG requires more electrodes than for the adult.

[1]  M. Letts,et al.  A biomechanical analysis of halo fixation in children. , 1988, The Journal of bone and joint surgery. British volume.

[2]  D. G. Watts,et al.  Spectral analysis and its applications , 1968 .

[3]  William R. Reynolds,et al.  Block-matching algorithm for mitigating aliasing effects in undersampled image sequences , 2002 .

[4]  J Sampalis,et al.  Ultrasound in the assessment of cranial bone thickness. , 1997, The Journal of craniofacial surgery.

[5]  Don M. Tucker,et al.  Localizing Acute Stroke-related EEG Changes:: Assessing the Effects of Spatial Undersampling , 2001, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[6]  Ramesh Srinivasan,et al.  Estimating the spatial Nyquist of the human EEG , 1998 .

[7]  Don M. Tucker,et al.  Regional head tissue conductivity estimation for improved EEG analysis , 2000, IEEE Transactions on Biomedical Engineering.

[8]  P. Nunez,et al.  Spherical harmonic decomposition applied to spatial-temporal analysis of human high-density electroencephalogram. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  C. Hansman,et al.  Growth of interorbital distance and skull thickness as observed in roentgenographic measurements. , 1966, Radiology.

[10]  E. Harth,et al.  Electric Fields of the Brain: The Neurophysics of Eeg , 2005 .

[11]  木村 充 A.Papoulis: The Fourier Integral and its Applications. McGraw-Hill, New York 1962, 306頁, 15×23cm, $12.00. , 1963 .

[12]  G. Wahba Spline models for observational data , 1990 .

[13]  T. Pedley Current Practice of Clinical Electroenceph‐alography , 1980, Neurology.

[14]  Mingni Sun,et al.  An efficient algorithm for computing multishell spherical volume conductor models in EEG dipole source localization. , 1997, IEEE transactions on bio-medical engineering.

[15]  O Bertrand,et al.  A theoretical justification of the average reference in topographic evoked potential studies. , 1985, Electroencephalography and clinical neurophysiology.

[16]  P. Nunez,et al.  Spatial filtering and neocortical dynamics: estimates of EEG coherence , 1998, IEEE Transactions on Biomedical Engineering.

[17]  Ronald G Emerson,et al.  Spatial correlation of the infant and adult electroencephalogram , 2003, Clinical Neurophysiology.

[18]  Carl E. Halford,et al.  Guest Editorial: Special Section on Sampled Imaging Systems , 1999 .

[19]  K R Kattan,et al.  Thickness of the normal skull in the American Blacks and Whites. , 1975, American journal of physical anthropology.

[20]  Zia-ur Rahman,et al.  Fidelity analysis of sampled imaging systems , 1999 .

[21]  Prashant D. Sardeshmukh,et al.  Spatial Smoothing on the Sphere , 1984 .

[22]  Ronald G. Driggers,et al.  Influence of sampling on target recognition and identification , 1999 .

[23]  A. Papoulis,et al.  The Fourier Integral and Its Applications , 1963 .

[24]  S. K. Law,et al.  Thickness and resistivity variations over the upper surface of the human skull , 2005, Brain Topography.

[25]  M Hallett,et al.  A method for determining optimal interelectrode spacing for cerebral topographic mapping. , 1989, Electroencephalography and clinical neurophysiology.

[26]  D. Tucker,et al.  Spatial sampling and filtering of EEG with spline Laplacians to estimate cortical potentials , 2005, Brain Topography.

[27]  Dennis M. Healy,et al.  Asymptotically fast algorithms for spherical and related transforms , 1989, 30th Annual Symposium on Foundations of Computer Science.

[28]  Ta-Hsin Li,et al.  Aliasing Effects and Sampling Theorems of Spherical Random Fields when Sampled on a Finite Grid , 1997 .

[29]  W. Freeman,et al.  Spatial spectra of scalp EEG and EMG from awake humans , 2003, Clinical Neurophysiology.

[30]  W. Fulks Advanced Calculus: An Introduction to Analysis , 1969 .

[31]  Zia-ur Rahman,et al.  Information-theoretic assessment of sampled imaging systems , 1999 .

[32]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1987 .

[33]  D. Healy,et al.  Computing Fourier Transforms and Convolutions on the 2-Sphere , 1994 .

[34]  G. Arfken Mathematical Methods for Physicists , 1967 .

[35]  D. Tucker Spatial sampling of head electrical fields: the geodesic sensor net. , 1993, Electroencephalography and clinical neurophysiology.

[36]  Mali Gong,et al.  Aliasing in minification of digital images , 2001 .

[37]  G. R. Shaw,et al.  Spherical harmonic analysis of the electroencephalogram , 1989, Sixth Multidimensional Signal Processing Workshop,.

[38]  A. Fernández-Nieves,et al.  Structure formation from mesoscopic soft particles. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

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