Importance of the class of harmonic sources in the identification of sources in the inverse electroencephalographic problem


volume conductor model
harmonic sources
equivalent sources
inverse electroencephalographic problema
admissible data method
brain volume
allowable measurements
mathematical theorems
cerebral cortex
sources modelo de medio conductor
fuentes armónicas
fuentes equivalentes
problema inverso electroencefalográfico
método de datos admisibles
volumen cerebral
mediciones admisibles
cuero cabelludo
teoremas matemáticos
corteza cerebral

How to Cite

Mozqueda Lafarga, J., Fraguela Collar, A., Soto Bajo, M., & Herrera Vega, J. (2020). Importance of the class of harmonic sources in the identification of sources in the inverse electroencephalographic problem. Nova Scientia, 12(24).


Introduction: In this work we discuss the relevance of the harmonic sources on the brain volume, which reproduce a given potential distribution on the scalp. These sources, apart from being a unicity class, they play a fundamental role in the resolution of the inverse problem of source identification with respect to any other sources class.

Method: We make use of the volume conductor model for the head, in order to relate sources and reproduced measurements. The problem is rewritten as an operational formulation which allows to characterize the admissible measurements with respect to any considered sources class.

Results: The admissible data set is characterized for the harmonic sources class on the brain volume. Also, the importance of this class in the context of the source estimation problem, with respect to any sources class, is shown. This is specifically illustrated considering the class of harmonic sources on a neighborhood of the cortex. Moreover, it is also shown the role the harmonic sources class on the brain plays when applying the Admissible Data Method (ADM) in order to get a general regularization scheme for the source estimation problem with respect to a unicity sources class.

Conclusion: A general resolution methodology for the source estimation problem in the context of the inverse electroencephalographic problem is proposed, in which the harmonic sources class on the brain volume is crucial. Namely, given an arbitrary sources unicity class (for this inverse problem), a general method is developed for identifying the source in this class whose reproduced potential distribution best approximates a given potential measurement on the scalp. We consider sources classes in connection with the electrical activity near the cortex.


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