Partial independence of bioelectric and biomagnetic fields and its implications for encephalography and cardiography

Abstract

In this article, we clearly demonstrate that the electric potential and the magnetic field can contain different information about current sources in three-dimensional conducting media. Expressions for the magnetic fields of electric dipole and quadrupole current sources immersed in an infinite conducting medium are derived, and it is shown that two different point dipole distributions that are electrically equivalent have different magnetic fields. Although measurements of the electric potential are not sufficient to determine uniquely the characteristics of a quadrupolar source, the radial component of the magnetic field can supply the additional information needed to resolve these ambiguities and to determine uniquely the configuration of dipoles required to specify the electric quadrupoles. We demonstrate how the process can be extended to even higher order terms in an electrically silent series of magnetic multipoles. In the context of a spherical brain source model, it has been mathematically demonstrated that the part of the neuronal current generating the electric potential lives in the orthogonal complement of the part of the current generating the magnetic potential. This implies a mathematical relationship of complementarity between electroencephalography (EEG) and magnetoencephalography (MEG), although the theoretical result in question does not apply to the non-spherical case (Dassios (2008), Math Med Biol, vol. 25, p. 133). Our results have important practical applications in cases where electrically silent sources that generate measurable magnetic fields are of interest. Moreover, electrically silent, magnetically active moments of higher order can be useful when cancellation due to superposition of fields can occur, since this situation leads to a substantial reduction in the measurable amplitude of the signal. In this context, information derived from magnetic recordings of electrically silent, magnetically active multipoles can supplement electrical recordings for the purpose of studying the physiology of the brain. Magnetic fields of the electric multipole sources in a conducting medium surrounded by an insulating spherical shell are also presented and the relevance of this calculation to cardiographic and encephalographic experimentation is discussed.

Traumatic Brain Injury Detection Using Electrophysiological Methods

“…These features may be contrary to simple, lightweight devices capable of field-based use and easy operation. Additionally, the signal analysis and neuroinformatics challenges of these investigations should not be underestimated (Irimia et al, 2009 , 2012 ; Goh et al, 2014 ).…”

Forward and inverse electroencephalographic modeling in health and in acute traumatic brain injury

“…The process of computing the electric potentials produced at the scalp due to current sources in the brain is known as the forward problem of bioelectricity, whereas the process of localizing brain activity based on scalp EEG measurements is referred to as the inverse problem (Irimia et al, 2009; Lima et al, 2006). Despite the potential clinical usefulness of EEG source localization in acute TBI, there is a disappointing paucity of studies which have explored this topic.…”

Algebraic Reconstruction of Current Dipoles and Quadrupoles in Three-Dimensional Space

“…Recently, a new method, the multipolar representation of the source, has been developed that incorporates some of the advantages of the above two methods, and has attracted considerable attention [13][14][15][16][17][18]. In this model, instead of expressing the current source by an equivalent current dipole, an equivalent dipole and quadrupole [15,16] or an equivalent dipole and octopole [13,14] are used where the quadrupole or octopole is determined depending on the spatial extent of the support of the current source.…”