Spherical splines and average referencing in scalp electroencephalography

Brain Topography

Volumn 19, Issue 1-2, 2006, Pages 43-52

  Ferree, Thomas C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

EEG; Interpolation; Reference; Skull conductivity; Topographic map

Indexed keywords

ARTICLE; BRAIN MAPPING; DENSITY; DIPOLE; ELECTRIC POTENTIAL; ELECTRODE; ELECTROENCEPHALOGRAPHY; HYPOTHESIS; MATHEMATICAL ANALYSIS; MODEL; PRIORITY JOURNAL; SCALP; SIMULATION;

BRAIN MAPPING; ELECTRIC CONDUCTIVITY; ELECTRODES; ELECTROENCEPHALOGRAPHY; HUMANS; MODELS, NEUROLOGICAL; SCALP; SKULL;

EID: 33845541788     PISSN: 08960267     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10548-006-0011-0     Document Type: Article

References (35)

1. Arfken, G.B. and Weber, H.J. Mathematical Methods for Physicists. Academic Press, 1995.
2. Baumann, S.B., Wonzy, D.R., Kelly, S.K. and Meno, F.M. The electrical conductivity of human cerebrospinal fluid at body temperature. IEEE Trans. Biomed. Eng., 1997, 44(3): 220-223.
3. Bertrand, O., Perrin, F. and Pernier, J. A theoretical justification of the average reference in topographic evoked potential studies. Electroenceph. Clin. Neurophysiol., 1985, 62(6): 462-464.
4. Burger, H.C. and van Milaan, J.B. Measurements of the specific resistance of the human body to direct current. Acta Med. Scand. Fasc. VI, 1943, 114: 584-607.
5. Desmedt, J.E. and Tomberg, C. Topographic analysis in brain mapping can be compromised by the average reference. Brain Topogr., 1990, 3(1): 35-42.
6. Duchon, J. Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. RAIRO Anal. Num., 1976, 10: 5-12.
7. Fletcher, E.M., Kussmaul, C.L. and Mangun, G.R. Estimation of interpolation errors in scalp topographic mapping. Electroenceph. Clin. Neurophysiol., 1996, 98: 422-434.
8. Gencer, N.G., Williamson, S.J., Gueziec, A. and Hummel, R. Optimal reference electrode selection for electric source imaging. Electroenceph. Clin. Neurophysiol., 1996, 99(2): 163-173.
9. Geselowitz, D.B. The zero of potential. IEEE Eng. Med. Biol. Mag., 1998, 17(1): 128-132.
10. Hamalainen, M.S. and Sarvas, J. Realistic conductor geometry model of the human head for interpretation of neuromagnetic data. IEEE Trans. Biomed. Eng., 1989, 36: 165-171.
11. Hjorth, B. An on-line transformation of EEG scalp potentials into orthogonal source derivations. Electroenceph. Clin. Neurophysiol., 1975, 39: 526-530.
12. Junghofer, M., Elbert, T., Tucker, D.M. and Braun, C. The polar average reference effect: A bias in estimating the head surface integral in EEG recording. Clin. Neurophysiol., 1999, 110(6): 1149-1155.
13. Law, S.K., Nunez, P.L. and Wijesinghe, R.S. High-resolution EEG using spline generated surface Laplacians on spherical and ellipsoidal surfaces. IEEE Trans. Biomed. Eng., 1993, 40(2): 145-153.
14. Lehmann, D., Ozaki, H. and Pal, I. Averaging of spectral power and phase via vector diagram best fits without reference electrode or reference channel. Electroencephalogr. Clin. Neurophysiol., 1986, 64(4): 350-363.
15. Nunez, P.L. Electric fields of the brain: The neurophysics of EEG. New York, Oxford University Press, 1981.
16. Nunez, P.L. and Srinivasan, R. Electric fields of the brain: The neurophysics of EEG, 2nd edition. New York, Oxford University Press, 2006.
17. Nunez, P.L., Srinivasan, R., Westdorp, A.F., Wijesinghe, R.S., Tucker, D.M., Silberstein, R.B. and Cadusch, P.J. EEG coherency. I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and interpretation at multiple scales. Electroencephalogr. Clin. Neurophysiol., 1997, 103(5): 499-515.
18. Orekhova, E.V., Wallin, B.G. and Hedstrom, A. Modification of the average reference montage: Dynamic average reference. J. Clin. Neurophysiol., 2002, 19(3): 209-218.
19. Perrin, F., Pernier, J., Bertrand, O., Giard, M.H. and Echallier, J.F. Mapping of scalp potentials by surface spline interpolation. Electroenceph. Clin. Neurophysiol., 1987, 66: 75-81.
20. Perrin, F., Pernier, J., Bertrand, O. and Echallier, J.F. Spherical splines for scalp potential and current density mapping. Electroenceph. Clin. Neurophysiol., 1989, 72: 184-187.
21. Perrin, F., Pernier, J., Bertrand, O. and Echallier, J.F. Corrigenda: EEG 02274. Electroenceph. Clin. Neurophysiol., 1990, 76: 565.
22. Press, W.H., Tuekolsky, S.A., Vetterling, W.T. and Flannery, B.P. Numerical recipes in C. Cambridge University Press, 1992.
23. Rush, S. and Blanchard, R.R. Skull physical and electrical characteristics relevant to the distribution from electrodes on the scalp. Proceedings of the 19th ACEMB, 1966.
24. Rush, S. and Driscoll, D.A. Current distribution in the brain from surface electrodes. Anesthesia analgesia, 1968, 47(6): 717-723.
25. Salu, Y., Cohen, L.G., Rose, D., Sato, S., Kufta, C. and Hallett, M. An improved method for localizing electric brain dipoles. IEEE Trans. Biomed. Eng., 1990, 37: 699-705.
26. Soong, A.C.K., Lind, J.C., Shaw, G.R. and Koles, Z.J. Systematic comparisons of interpolation techniques in topographic brain mapping. Electroenceph. Clin. Neurophysiol., 1993, 87: 185-195.
27. Soufflet, L., Toussaint, 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. Neurophys., 1991, 79: 393-402.
28. Srinivasan, R., Tucker, D.M. and Murias, M. Estimating the spatial Nyquist of the human EEG. Behav. Res. Methods, Instrum. Comput., 1998, 30: 8-19.
29. Stok, C.J. The influence of model parameters on EEG/MEG single dipole source estimation. IEEE Trans. Biomed. Eng., 1987, 34(4): 289-296.
30. Sun, M. An efficient algorithm for computing multishell spherical volume conductor models in EEG dipole source localization. IEEE Trans. Biomed. Eng., 1997, 44(12): 1243-1252.
31. Tomberg, C., Neol, P., POzaki, I. and Desmedt, J.E. Inadequacy of the average reference for the topographicmapping of focal enhancements of brain potentials. Electroenceph. Clin. Neurophys., 1990, 77(4): 259-265.
32. Wahba, G. and Wendelberger, J. Some new mathematical methods for variational objective analysis using splines and cross validation. Mon. Weather Rev., 1980, 108: 1122-1143.
33. Wahba, G. Spline interpolation and smoothing on the sphere. SIAM J. Sci. Stat. Comput., 1981, 2(1): 5-16.
34. Wahba, G. Erratum: Spline interpolation and smoothing on the sphere. SIAM J. Sci. Stat. Comput. 1982, 3(3): 385-386.
35. Yao, D. A. method to standardize a reference of scalp EEG recordings to a point at infinity. Physiol. Meas., 2001, 22(4): 693-711.