A theoretical formulation of the electrophysiological inverse problem on the sphere

Physics in Medicine and Biology

Volumn 51, Issue 7, 2006, Pages 1737-1758

  Riera, Jorge J ^a   Valdés, Pedro A ^b   Tanabe, Kunio ^c   Kawashima, Ryuta ^a  

^a TOHOKU UNIVERSITY   (Japan)

^b CUBAN NEUROSCIENCE CENTER   (Cuba)

^c INSTITUTE OF STATISTICAL MATHEMATICS   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CURRENT DENSITY; ELECTRIC POTENTIAL; FACE RECOGNITION; IMAGING TECHNIQUES; NEUROLOGY; TOMOGRAPHY;

BAYES INFORMATION; NON-HARMONIC COMPONENTS; REPRODUCING KERNEL HILBERT SPACES (RKHS) FORMALISM;

INVERSE PROBLEMS;

ARTICLE; CALCULATION; DENSITY; ELECTRIC POTENTIAL; ELECTROENCEPHALOGRAM; ELECTROPHYSIOLOGY; MAGNETOENCEPHALOGRAPHY; NERVE CONDUCTION; NEUROIMAGING; PRIORITY JOURNAL; RECOGNITION; TECHNIQUE; THEORETICAL MODEL; THREE DIMENSIONAL IMAGING;

ALGORITHMS; BRAIN MAPPING; COMPUTER SIMULATION; ELECTROENCEPHALOGRAPHY; HEAD; HUMANS; IMAGING, THREE-DIMENSIONAL; MAGNETOENCEPHALOGRAPHY; MODELS, BIOLOGICAL;

EID: 33645314425     PISSN: 00319155     EISSN: 13616560     Source Type: Journal    
DOI: 10.1088/0031-9155/51/7/007     Document Type: Article

References (36)

1. Akaike H 1986 The selection of smoothing priors for distributed lag estimation Bayesian Inference and Decision Techniques ed P Goel and A Zellner (Amsterdam: Elsevier) pp 109-18
2. Axler S, Bourdon P and Ramey W 2001 Harmonic Function Theory (New York: Springer)
3. Baillet S and Garnero L 1997 A Bayesian approach to introducing anatomo-functional priors in the EEG/MEG inverse problem IEEE Trans. Biomed. Eng. 44 374-85
4. Baillet S, Marin G, Garnero L and Hugonin J P 1999 Combined MEG and EEG source imaging by minimization of mutual information IEEE Trans. Biomed. Eng. 46 522-34
5. Baillet S, Riera J, Mangin J F, Garnero L and Aubert E 2001 Evaluation of inverse methods and head models for EEG source localization using a human skull phantom Phys. Med. Biol. 46 77-96
6. Cabo A, Handy C and Bessis D 2001 On the uniqueness of the surface sources of evoked potentials Phys. Rev. E 64 1-10
7. Cohen D and Cuffin B N 1983 Demonstration of useful differences between magnetoencephalogram and electroencephalogram Electroencephalogr. Clin. Neurophysiol. 56 38-51
8. Díaz D, Martínez J M and Riera J 1998 Electric field induced inside a sphere due to radial single coil magnetic stimulation Proc. 4th Int. Conf. Human Brain Mapping. Neuroimage 7 S633
9. Fokas A S, Gel-fand I M and Kurylev Y 1996 Inversion method for magnetoencephalography Inverse Problems 12 L9-L11
10. Fokas A S, Kurylev Y and Marinakis V 2004 The unique determination of neuronal currents in the brain via magnetoencephalography Inverse Problems 20 1067-82
11. Fuchs M, Wagner M, Wischmann H-A, Köhler T, Theiβen A, Drenckhahn R and Buchner H 1998 Improving source reconstructions by combining bioelectric and biomagnetic data Electroencephalogr. Clin. Neurophysiol. 107 93-111
12. Good I J 1965 The Estimation of Probabilities (Cambridge, MA: MIT Press)
13. Gorodnitsky I F, George J S and Rao B D 1995 Neuromagnetic imaging with FOCUSS: a recursive weighted minimum norm algorithm Electroencephalogr. Clin. Neurophysiol. 95 231-51
14. Grynszpan F and Geselowitz D 1973 Model studies of the magnetocardiogram Biophys. J. 13 911-25
15. Hadamard J 1923 Lecture on the Cauchy Problem in Linear Partial Differential Equations (New Haven, CT: Yale University Press)
16. Hamalainen M S and Ilmoniemi R J 1994 Interpreting magnetic fields of the brain: minimum norm estimates Med. Biol. Eng. Comput. 32 35-42
17. Hasson R and Swithenby S J 1999 A Bayesian test for the appropriateness of a model in the biomagnetic inverse problem Inverse Problems 15 1439-54
18. Helmholtz H 1853 Über einige Gestz der Vertheilung elektrisher Ströme in KörperlichenLeitern, mit Anwendung auf die thierischelektrischen Versuche Ann. Phys. Chem. 3 211-33
19. Helmholtz H 1853 Über einige Gestz der Vertheilung elektrisher Ströme in KörperlichenLeitern, mit Anwendung auf die thierischelektrischen Versuche Ann. Phys. Chem. 3 353-77
20. Ioannides A A, Bolton J P R and Clarke C J S 1990 Continuous probabilistic solutions to the biomagnetic inverse problem Inverse Problems 6 523-42
21. Jackson J D 1975 Classical Electrodynamics (New York: Wiley)
22. Jerbi K, Mosher J C and Leahy R M 2002 On MEG forward modeling using multipolar expansions Phys. Med. Biol. 47 523-55
23. Kimeldorf G and Wahba G 1971 Some results on Tchebycheffian spline functions J. Math. Anal. Appl. 33 82-95
24. Kitagawa G and Gersch W 1984 A smoothness prior-state modeling of time series with trend and seasonality J. Am. Stat. Assoc. 79 378-89
25. Morse F M and Fesbasch H 1953 Methods of Theoretical Physics (New York: McGraw-Hill)
26. Nakamura K et al 2000 Functional delineation of the human occipito-temporal areas related to face and scene processing: a PET study Brain 123 1903-12
27. Pascual-Marqui R D 1994 Low-resolution electromagnetic tomography: a new method for localizing electrical activity in the brain Int. J. Psychophysiol. 18 49-65
28. Riera J J and Fuentes M E 1998 Electric lead field for a piece-wise homogeneous volume conductor model of the head IEEE Trans. Biomed. Eng. 45 746-53
29. Riera J J, Fuentes M E, Valdés P A and Oharriz Y 1998 EEG distributed inverse solution for a spherical head model Inverse Problems 14 1009-19
30. Riera J J, Wan X, Jimenez J C and Kawashima R 2006 Nonlinear local electro-vascular coupling: Part I. A theoretical model Human Brain Mapping at press
31. Rush S and Driscoll D A 1969 EEG electrode sensitivity-an application of reciprocity IEEE Trans. Biomed. Eng. 16 15-22
32. Sato N, Nakamura K, Nakamura A, Sugiura M, Ito K, Fukuda H and Kawashima R 1999 Different time course between scene processing and face processing: a MEG study Neuroreport 10 3633-7
33. Tanabe K, Sagae M and Ueda S 1988 BNDE, FORTRAN Subroutines for Bayesian Nonparametric Univariate and Bivariate Density Estimators (Comp. Sci. Monogr. vol 24) ed T Komazawa et al (Tokyo: The Institute of Statistical Mathematics) pp 1-52
34. Trujillo-Barreto N J, Aubert-Vazquez E and Valdes-Sosa P A 2004 Bayesian model averaging in EEG/MEG imaging. Neuroimage 21 1300-19
35. Wahba G 1990 Spline models for observational data CBMS-NSF Regional Conf. Ser. App. Math. vol 59 (Philadelphia: SIAM)
36. Yamashita O, Galka A, Ozaki T, Biscay R and Valdes-Sosa P 2004 Recursive penalized least squares solution for dynamical inverse problems of EEG generation Human Brain Mapp. 21 221-35