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Model Studies of the Magnetocardiogram

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Grynszpan, Flavio, Geselowitz, David B.·1973·Biophysical Journal

DOI 10.1016/s0006-3495(73)86034-5PMC PMC1484372

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Abstract

A general expression is developed for the quasi-static magnetic field outside an inhomogeneous nonmagnetic volume conductor containing internal electromotive forces. Multipole expansions for both the electric and magnetic fields are derived. It is shown that the external magnetic field vanishes under conditions of axial symmetry. The magnetic field for a dipole current source in a sphere is derived, and the effect of an eccentric spherical inhomogeneity is analyzed. Finally the magnetic dipole moment is calculated for a current dipole in a conducting prolate spheroid.

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Background
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Background
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Method
Cancellation of EEG and MEG Signals Generated by Extended and Distributed Sources
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Background
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“4) reduces to [6]–[8] B = μ0∇U, U(x) = 1 4π ∫”
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“N IH -PA Author M anuscript N IH -PA Author M anuscript N IH -PA Author M anuscript that radial primary currents in a spherically symmetric volume conductor do not produce external magnetic fields (Baule and McFee, 1965, Grynszpan and Geselowitz, 1973).”
Background
On MEG forward modelling using multipolar expansions
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BackgroundMethodInfluential
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“However, MEG measurement is not capable of recording cortical activation of gyri where the electric current generated is oriented vertically to the brain surface (Gryzpan and Geselowitz, 1973).”
Background
BabyMEG: A whole-head pediatric magnetoencephalography system for human brain development research.
Okada, Y., Hämäläinen, M., Pratt, K., Mascarenas, A., Miller, P., Han, M.-L., Robles, J., Cavallini, A., Power, B., Sieng, K., et al. (2016) · Review of Scientific Instruments · doi:10.1063/1.4962020 · Cited by 76
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Background
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Background
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Background
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BackgroundMethod
Multichannel SQUID Biomagnetic Systems
Vrba, J. (2000) · Springer eBooks · doi:10.1007/978-94-017-0752-7_2 · Cited by 63
“The magnetic field of an equivalent current dipole in a spherical medium can be computed analytically [62, 63].”
Background
Magnetic localisation of intracranial dipoles: simulation with a physical model.
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Analysis of MEG signals of spreading cortical depression with propagation constrained to a rectangular cortical strip. I. Lissencephalic rabbit model.
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MAGNETIC LOCATION OF CORTICAL ACTIVITY *
Williamson, S. (1980) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1982.tb50792.x · Cited by 58
Invariance in current dipole moment density across brain structures and species: Physiological constraint for neuroimaging
Murakami, S., & Okada, Y. C. (2015) · NeuroImage · doi:10.1016/j.neuroimage.2015.02.003 · Cited by 55
“separating regions of differing electrical conductivities (Geselowitz, 1970; Geselowtitz, 1973; Grynszpan and Geselowitz, 1973; Plonsey, 1972).”
Somatotopic organization of the human somatosensory cortex revealed by neuromagnetic measurements
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“Tile assumption that only the tangential component of the dipole contributes to B~ is based on the theoretical result obtained by Geselowitz (1970) and Grynszpan and Geselowitz (1973) for a spherical conducting medium whose conductivity may vary with radial distance from the center.”
Background
Differential characterization of neural sources with the bimodal truncated SVD pseudo-inverse for EEG and MEG measurements
Gencer, N., & Williamson, S. J. (1998) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.686790 · Cited by 55
Advantages and limitations of magnetic source imaging
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“The spherical model has provided a convenient simplification for modeling the pertinent region of the head when interpreting neuromagnetic data (Grynszpan and Geselowitz 1973; Cuffin and Cohen 1977).”
Background
Inversion method for magnetoencephalography
Fokas, A., Gel'fand, I., & Kurylev, Y. (1996) · doi:10.1088/0266-5611/12/3/001 · Cited by 53
Magnetic field of the human sensorimotor cortex
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Source Cancellation Profiles of Electroencephalography and Magnetoencephalography
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“The most important difference in how signals are cancelled differently in EEG and MEG is a consequence of the fact that MEG is preferentially sensitive to source orientation (Cuffin, 1990; Grynszpan and Geselowitz, 1973; Hamalainen et al., 1993).”
Automatic activation in the human primary motor cortex synchronized with movement preparation
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“…spherical shells, Boundary Element Model (BEM), and Finite Element Model (FEM) are among the most widely used (Fuchs et al. 1998; Buchner et al. 1997; Yan et al. 1991; Hämäläinen and Sarvas 1989; Sarvas 1987; Stock 1986; Meijs et al. 1985; Grynszpan and Gezelowitz 1973; Barnard et al. 1967).”
Method
Inverse solutions based on MEG and EEG applied to volume conductor analysis.
Stok, C. J., Meijs, J. W. H., & Peters, M. (1987) · Physics in Medicine and Biology · doi:10.1088/0031-9155/32/1/015 · Cited by 49
Temporal structure of implicit motor imagery in visual hand‐shape discrimination as revealed by MEG
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Tackling magnetoencephalography with particle swarm optimization
Parsopoulos, K. E., Kariotou, F., Dassios, G., & Vrahatis, M. N. (2009) · International Journal of Bio-Inspired Computation · doi:10.1504/ijbic.2009.022772 · Cited by 46
“This is possible by capturing and studying the magnetic fields produced by excitations of small regions of the brain, using sensor measurements (Bronzan, 1971; Dassios, 2006, 2007, 2008a, 2008b; Dassios and Fokas, 2008a; Dassios et al., 2005, 2007a, 2007b; Dassios and Kariotou, 2003a, 2003b, 2004, 2005; Fokas et al.,…”
Method
Distortion of magnetic evoked fields and surface potentials by conductivity differences at boundaries in brain tissue.
Huang, J.-C., Nicholson, C., & Okada, Y. C. (1990) · Biophysical Journal · doi:10.1016/s0006-3495(90)82635-7 · Cited by 46
“Because the secondary sources are directed normal to the boundary surface, the magnetic field due to the secondary sources at the scalp and skull should be parallel to their respective tangential plane of the boundary containing the secondary sources (Grynszpan and Geselowitz, 1973).”
Background
Magnetic evoked field associated with transcortical currents in turtle cerebellum.
Okada, Y., & Nicholson, C. (1988) · Biophysical Journal · doi:10.1016/s0006-3495(88)83153-9 · Cited by 46
Characterization of the human auditory cortex by the neuromagnetic method
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Human fetal brain imaging by magnetoencephalography: verification of fetal brain signals by comparison with fetal brain models
Vrba, J., Robinson, S., McCubbin, J., Murphy, P., Eswaran, H., Wilson, J. D., Preissl, H., & Lowery, C. (2004) · NeuroImage · doi:10.1016/j.neuroimage.2003.10.022 · Cited by 44
Measurement of the human magnetic heart vector.
Barry, W. H., Fairbank, W., Harrison, D., Lehrman, K. L., Malmivuo, J., & Wikswo, J. (1977) · Science · doi:10.1126/science.929192 · Cited by 41
MEG source models and physiology.
Okada, Y., Lauritzen, M., & Nicholson, C. (1987) · Physics in Medicine and Biology · doi:10.1088/0031-9155/32/1/007 · Cited by 40
Dependence of the MEG on dipole orientation in the rabbit head.
Melcher, J., & Cohen, D. (1988) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/0013-4694(88)90024-7 · Cited by 39
Biomagnetism: The First Sixty Years
Roth, B. J. (2023) · Sensors · doi:10.3390/s23094218 · Cited by 59
Laterality of human primary gustatory cortex studied by MEG.
Onoda, K., Kobayakawa, T., Ikeda, M., Saito, S., & Kida, A. (2005) · Chemical Sensors · doi:10.1093/chemse/bji059 · Cited by 38
“For estimates of the equivalent current dipoles (ECDs), we attempted to minimize the estimation error by using the equation of Grynszpan–Geselowitz (Grynszpan and Geselowitz, 1973).”
Spike and slow wave localization by magnetoencephalography.
Lewine, J., & Orrison, W. (1995) · Neuroimaging clinics of North America · doi:10.1016/s1052-5149(25)00325-9 · Cited by 38
Magnetic field associated with neural activities in an isolated cerebellum.
Okada, Y., Lauritzen, M., & Nicholson, C. (1987) · Brain Research · doi:10.1016/0006-8993(87)91451-x · Cited by 38
Hemispheric asymmetry of the auditory evoked N100m response in relation to the crossing point between the central sulcus and Sylvian fissure.
Ohtomo, S., Nakasato, N., Kanno, A., Hatanaka, K., Shirane, R., Mizoi, K., & Yoshimoto, T. (1998) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/s0168-5597(97)00065-8 · Cited by 37
The reliability of the fetal magnetocardiogram
Stinstra, J. (2001) · doi:10.3990/1.9789036516587 · Cited by 35
On cortical folds and neuromagnetic fields.
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SQUID instrumentation and the relative covariance method for magnetic 3D localization of pathological cerebral sources
Chapman, R., Romani, G., Barbanera, S., Leoni, R., Modena, I., Ricci, G., & Campitelli, F. (1983) · Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimento · doi:10.1007/bf02805209 · Cited by 35
Improving Lesion Conductivity Estimate by Means of EEG Source Localization Sensitivity to Model Parameter
Vatta, F., Bruno, P., & Inchingolo, P. (2002) · Journal of Clinical Neurophysiology · doi:10.1097/00004691-200201000-00001 · Cited by 32
“…of the effects of eccentric inhomogeneities on the EEG distribution has been accomplished almost only in terms of the forward problem (Cuffin, 1982; Grynszpan and Geselowitz, 1973; Kosugi et al., 1985; Ueno et al., 1987; van den Broek et al., 1998) and so, at present, there is a lack of…”
Background
Linear estimation theory applied to the reconstruction of a 3-D vector current distribution.
Smith, W. E., Dallas, W. J., Kullmann, W., & Schlitt, H. (1990) · Applied Optics · doi:10.1364/ao.29.000658 · Cited by 32
Effects of fissures in the brain on electroencephalograms and magnetoencephalograms
Cuffin, B. (1985) · doi:10.1063/1.335378 · Cited by 31
Round table. On the current multipole presentation of the primary current distributions
Katila, T. (1983) · Il Nuovo Cimento D · doi:10.1007/bf02455963 · Cited by 29
Striate cortical generators of the N75, P100 and N145 components localized by pattern reversal visual evoked magnetic fields.
Hatanaka, K., Nakasato, N., Seki, K., Kanno, A., Mizoi, K., & Yoshimoto, T. (1997) · Tohoku journal of experimental medicine · doi:10.1620/tjem.182.9 · Cited by 27
Overview of MEG
Ahlfors, S. P., & Mody, M. (2016) · Organizational Research Methods · doi:10.1177/1094428116676344 · Cited by 27
“…the head are almost exclusively generated by primary currents oriented tangentially with respect to the inner surface of the skull, whereas MEG is insensitive to radially oriented primary currents (Ahlfors, Han, Belliveau, & Hamalainen, 2010; Cohen & Cuffin, 1983; Grynszpan & Geselowitz, 1973).”
Representation of Salty Taste Stimulus Concentrations in the Primary Gustatory Area in Humans
Kobayakawa, T., Saito, S., Gotow, N., & Ogawa, H. (2008) · Chemosensory Perception · doi:10.1007/s12078-008-9030-4 · Cited by 27
“In our estimation of ECDs, we attempted to minimize error by using Grynszpan–Geselowitz’s equation (Grynszpan and Geselowitz 1973; see Kobayakawa et al. 1996).”
Method
Inferences concerning anatomy and physiology of the human brain based on its magnetic field
Okada, Y. C. (1983) · Il Nuovo Cimento D · doi:10.1007/bf02455940 · Cited by 24
The exterior magnetic field for the multilayer ellipsoidal model of the brain
Dassios, G., Giapalaki, S. N., Kandili, A. N., & Kariotou, F. (2007) · doi:10.1093/qjmam/hbl022 · Cited by 25
Locating accuracy of a current source of neuromagnetic responses: simulation study for a single current dipole in a spherical conductor.
Kuriki, S., Murase, M., & Takeuchi, F. (1989) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/0013-4694(89)90259-9 · Cited by 23
The magnetocardiogram
Roth, B. J. (2024) · Biophysics Reviews · doi:10.1063/5.0201950 · Cited by 23
Magnetocardiography: An Overview
Geselowitz, D. B. (1979) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.1979.326430 · Cited by 24
Self-citation
Spatiotemporal imaging of complexity
Robinson, S. E., Mandell, A. J., & Coppola, R. (2013) · Frontiers in Computational Neuroscience · doi:10.3389/fncom.2012.00101 · Cited by 20
“(11) Suitable methods for computing forward solutions include the current dipole in a homogeneously conducting sphere model (Grynszpan and Geselowitz, 1973; Sarvas, 1987; Hari et al., 1988), multiple local spheres fitted to the surface of the head (Huang et al., 1999), boundary element methods (De…”
Method
Jerk-locked back averaging and dipole source localization of magnetoencephalographic transients in a patient with epilepsia partialis continua.
Shigeto, H., Tobimatsu, S., Morioka, T., Yamamoto, T., Kobayashi, T., & Kato, M. (1997) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/s0013-4694(97)00040-0 · Cited by 21
Magnetic fields of the human brain
Williamson, S., & Kaufman, L. (1980) · Journal of Magnetism and Magnetic Materials · doi:10.1016/0304-8853(80)90405-9 · Cited by 21
Magnetoencephalography signals are influenced by skull defects.
Lau, S., Flemming, L., & Haueisen, J. (2014) · Clinical Neurophysiology · doi:10.1016/j.clinph.2013.12.099 · Cited by 20

Authors: Grynszpan, F., & Geselowitz, D. B.
Venue: Biophysical Journal
Publisher: Elsevier BV
Published: 1973-09
Volume: 13
Issue: 9
Pages: 911-925
ISSN: 0006-3495 (ISSN-L)
DOI: 10.1016/s0006-3495(73)86034-5
PMC: PMC1484372
OpenAlex: W2017229769
Cited by: 226
References: 0
Citations by year: 2026: 2 · 2024: 2 · 2023: 5 · 2020: 1 · 2019: 6 · 2017: 3 · 2016: 2 · 2015: 2 · 2014: 4 · 2013: 2 · 2012: 4
FWCI: 0.49
Type: journal article
Language: en
Open access: bronze
doi.org
Licence: www.elsevier.com/tdm/userlicense/1.0/ (tdm)
www.elsevier.com/open-access/userlicense/1.0/ (vor, 14563 d)
Locations: Biophysical Journal (publishedVersion)
PubMed Central (publishedVersion)
PubMed (publishedVersion)
Topics: Health Sciences › Medicine › Cardiology and Cardiovascular Medicine › ECG Monitoring and Analysis
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Atomic and Subatomic Physics Research
Physical Sciences › Engineering › Electrical and Electronic Engineering › Electrical and Bioimpedance Tomography
Keywords: magnetocardiogram, quasi-static magnetic field, volume conductor, multipole expansion, axial symmetry, prolate spheroid, magnetic dipole moment, cardiac magnetic field
MeSH terms: Conductometry, Heart, Magnetics, Mathematics, Models, Theoretical

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