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Model Studies of the Magnetocardiogram
Open accessAbstract
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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“a foundational research from the general theory of bioelectromagnetism describes the amount of potential additional information provided by MCG (1–7)”
From Clinical magnetocardiography: the unshielded bet—past, present, and future (2023) · cites this paper as [3]
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Effects of cavities on EEG dipole localization and their relations with surface electrode positions.
He, B., & Musha, T. (1989) · International Journal of Bio-Medical Computing · doi:10.1016/0020-7101(89)90022-6 · Cited by 20
Kaufman, L., Okada, Y. C., TRIPP, J., & Weinberg, H. (1984) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1984.tb23596.x · Cited by 19
A Model for Frequency Dependence of Conductivities of the Live Human Skull
Akhtari, M., Bryant, H., Emin, D., Merrifield, W., Mamelak, A., Flynn, E., Shih, J. J., Mandelkern, M., Matlachov, A., Ranken, D., et al. (2004) · Brain Topography · doi:10.1023/a:1025658432696 · Cited by 20
“…Boundary Element Model (BEM), and Finite Element Model (FEM) are among the most widely used (Fuchs et al. 1998; Buchner et al. 1997; Haueisen 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).”
MethodBanerjee, A., Tognoli, E., Assisi, C. G., Kelso, J. A. S., & Jirsa, V. (2008) · NeuroImage · doi:10.1016/j.neuroimage.2008.04.260 · Cited by 22
“…at anatomically motivated locations and comparing subsequently generated forward solution with the event related signal (Geselowitz, 1967; Grynszpan and Geselowitz, 1973; Hämäläinen and Sarvas, 1989; Mosher et al., 1999; Jirsa et al., 2002) 2) mode decomposition techniques that do not…”
BackgroundMagnetic fields produced by single motor units in human skeletal muscles.
Masuda, T., Endo, H., & Takeda, T. (1999) · Clinical Neurophysiology · doi:10.1016/s1388-2457(98)00021-2 · Cited by 19
MCG simulations with a realistic heart-torso model
Ramon, C., Czapski, P., Haueisen, J., Huntsman, L., Nowak, H., Bardy, G., Leder, U., Kim, Y., & Nelson, J. (1998) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.725329 · Cited by 19
“Earlier the modeling of the MCG was done using a current dipole in a prolate spheroidal model of the heart [7], [ 8 ].”
MethodRelative influence of model assumptions and measurement procedures in the analysis of the MEG
Meijs, J. W. H., Peters, M., Boom, H., & da Silva, F. L. (1988) · Medical and Biological Engineering and Computing · doi:10.1007/bf02442255 · Cited by 19
Gaetz, W., Gordon, R., Papadelis, C., Fujiwara, H., Rose, D., Edgar, J., Schwartz, E., & Roberts, T. (2015) · Journal of Pediatric Epilepsy · doi:10.1055/s-0035-1563726 · Cited by 18
Current and emerging potential for magnetoencephalography in pediatric epilepsy
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“Magnetic fields produced by radial sources do not usually come out to the surface of the head [29,43–45].”
BackgroundFilter functions for computing multipole moments from the magnetic field normal to a plane.
Alvarez, R. (1991) · IEEE Transactions on Medical Imaging · doi:10.1109/42.97587 · Cited by 18
The effect of torso geometry on magnetocardiographic isofield maps.
Horáček, B., Purcell, C., Lamothe, R., Merritt, R., Kafer, C., Periyalwar, S., Dey, S., Leon, L. J., & Stroink, G. (1987) · Physics in Medicine and Biology · doi:10.1088/0031-9155/32/1/018 · Cited by 18
MAGNETIC LOCATION OF CORTICAL ACTIVITY *
Williamson, S. J. (1980) · Annals of the New York Academy of Sciences · doi:10.1111/j.1749-6632.1980.tb19357.x · Cited by 17
Wang, L., & Kuperberg, G. R. (2023) · Language Cognition and Neuroscience · doi:10.1080/23273798.2023.2223783 · Cited by 16
“Unlike the magnetic fi eld, the electric fi eld is smeared at the head surface (Geisler & Gerstein, 1961; Grynszpan & Geselowitz, 1973).”
An identification method of electric current dipoles in spherically symmetric conductor
Yamatani, K., Ohe, T., & Ohnaka, K. (2002) · doi:10.1016/s0377-0427(01)00507-6 · Cited by 16
Chapter 5: Multi-Squid Devices and Their Applications
Ilmoniemi, R., Knuutila, J., Ryhänen, T., & Seppä, H. (1989) · Progress in low temperature physics · doi:10.1016/s0079-6417(08)60044-x · Cited by 16
The magnetic field inside special conducting geometries due to internal current
Heller, L., Ranken, D., & Best, E. (2004) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2004.827554 · Cited by 15
“For a conductivity profile that is spherically symmetric about some origin, it was shown by Grynszpan and Geselowitz [ 4 ], Cuffin and Cohen [5], Ilmoniemi et al. [11], and Sarvas [3] that the -field outside the conductor can be obtained directly without solving for the electric potential.”
ResultKikuchi, Y., Endo, H., Yoshizawa, S., Kait, M., Nishimura, C., Tanaka, M., Kumagai, T., & Takeda, T. (1997) · NeuroReport · doi:10.1097/00001756-199705060-00020 · Cited by 15
Symmetry considerations in the quasi-static approximation of volume conductor theory
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Modulation of early auditory processing by visually based sound prediction
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Effects of inhomogeneous regions on electric potentials and magnetic fields: Two special cases
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Popescu, M., Popescu, E.-A., Gustafson, K. M., Drake, W. B., & Lewine, J. D. (2006) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.2006.883788 · Cited by 14
“With realistic models, radial components of the currents (which are otherwise “silent” in a spherical volume conductor) become detectable [ 53 ].”
BackgroundHansen, J., Ko, H.-W., Fisher, R., & Litt, B. (1988) · Physics in Medicine and Biology · doi:10.1088/0031-9155/33/1/010 · Cited by 12
“The theory for the magnetic field seen by a point magnetometer outside a conducting sphere was derived by Grynszpan and Geselowitz (1973) and later by 0031-9155/88/010105+07$02.50 @ 1988 IOP Publishing Ltd 105”
MethodInfluentialStimulus‐contrast‐induced biases in activation order reveal interaction between V1/V2 and human MT+
Maruyama, M., Palomo, D., & Ioannides, A. A. (2007) · Human Brain Mapping · doi:10.1002/hbm.20495 · Cited by 10
“Each MFT computation uses a spherical conductor model for the conductivity of head [Grynszpan and Geselowitz, 1973], with the center of the conducting sphere in each case chosen to fit the inner surface of the skull in the appropriate hemisphere.”
BackgroundMethodThe Effects of Torso Geometry on Magnetocardiographic Lead Fields
Cuffin, B. (1981) · IEEE Transactions on Biomedical Engineering · doi:10.1109/tbme.1981.324854 · Cited by 11
“For MCG's, the approximately planar back portion of the torso boundary should have little or no effect on the actual LF's [5].”
BackgroundComputer simulation of the human magnetocardiogram
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“Equivalent current dipoles (ECDs) were estimated to minimize estimation errors via Grynszpan−Geselowitz’s equation (Grynszpan and Geselowitz 1973; Kobayakawa et al 1996).”
MethodMagnetoencephalography in clinical epileptology and Epilepsy research
Baumgartner, C., & Deecke, L. (2005) · Brain Topography · doi:10.1007/bf01140589 · Cited by 9
“First, in contrast to electric fields magnetic fields are less distorted by the resistive properties of the skull and scalp (Cohen and Cuffin 1983; Grynszpan and Geselowitz 1973).”
BackgroundCurrent Dipole Localization Errors as a Function of the System Noise and the Number of Sensors
Matsuba, H., Vrba, J., & Cheung, T. (2000) · doi:10.1007/978-1-4612-1260-7_20 · Cited by 9
Magnetic measurements and modelling for the investigation of the human-heart conduction system
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“For estimates of the equivalent current dipoles (ECDs), we attempted to minimize the estimation error with Grynszpan-Geselowitz’s equation [11,12] using signals from all 64 SQUID sensors.”
MethodA theoretical formulation of the electrophysiological inverse problem on the sphere
Riera, J., Valdés, P., Tanabe, K., & Kawashima, R. (2006) · Physics in Medicine and Biology · doi:10.1088/0031-9155/51/7/007 · Cited by 8
“(11) The multipole moments can be evaluated from elements of N and M, respectively (Grynszpan and Geselowitz 1973). qEnms = 2Anγnm ∫ N1n−1( r) · JP ( r) d r3 qMnms = 1 rM γnm ∫ N1n−1( r) · ( r × JP ( r)) d r3.”
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A dipole model for Spreading Cortical Depression
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Biomagnetism: a new tool in sport and exercise science
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“The most common approach to the solution of this problem is to approximate the current distribution, which is assumed to be localized according to realistic anatomical and physiological constraints, using a finite number of current dipoles of differing magnitudes and orientations (Grynszpan and Gaselowitz, 1983; Roman…”
BackgroundA theory of the magnetic field from current monopoles
Ferguson, A. S., & Durand, D. (1992) · doi:10.1063/1.351005 · Cited by 7
Some tentative model considerations based on experimental neuromagnetic data
Særmark, K. (1983) · Il Nuovo Cimento D · doi:10.1007/bf02455944 · Cited by 5
Magnetoencephalography and Epilepsy
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Magnetic fields of current monopoles in special volume conductors
Ferguson, A. S., & Durand, D. (1991) · doi:10.1109/20.133289 · Cited by 6
Computer simulation of magnetic-field patterns from the human cardiac conduction system
Leoni, R., & Romani, G. (1982) · Il Nuovo Cimento D · doi:10.1007/bf02451066 · Cited by 6
Advances in Neuroimaging for Neurodegenerative Disease
Veldsman, M., & Egorova, N. (2017) · Advances in neurobiology · doi:10.1007/978-3-319-57193-5_18 · Cited by 9
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Influence of unfused cranial bones on magnetoencephalography signals in human infants
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Computer model studies of the magnetocardiogram
Cuffin, B., & Geselowitz, D. (1977) · Annals of Biomedical Engineering · doi:10.1007/bf02364017 · Cited by 5
“(1) by expanding the reciprocal of R in an appropr ia te power series in r, where r is the distance of the observat ion point f rom the coordinate sys tem origin, which m a y be t aken to be at the center of the hear t (Grynszpan and Geselowitz, 1973).”
BackgroundSelf-citationMEG and Multimodal Integration
Ahlfors, S. P. (2014) · Springer eBooks · doi:10.1007/978-3-642-33045-2_7 · Cited by 2
Model evaluation using electroencephalography and magnetoencephalography.
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The Mathematics of the Imaging Techniques of MEG, CT, PET and SPECT
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Magnetic field of current monopoles in prolate and oblate spheroid volume conductors
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“First, a current dipole can easily break down symmetries of a volume conductor due to its dipole orientation, making theoretical calculations of the magnetic field much more difficult [1], [ 7 ].”
BackgroundMoving dipole inverse solutions using MEGs measured on a plane over the head.
Cuffin, B. (1991) · Electroencephalography and Clinical Neurophysiology · doi:10.1016/0013-4694(91)90096-m · Cited by 4
Applications in Bioinformatics and Medical Informatics
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Cortical Auditory Evoked Magnetic Fields: Mapping of Time and Frequency Domain Aspects
Hoke, M., Lehnertz, K., Lütkenhöner, B., & Pantev, C. (1989) · doi:10.1007/978-3-642-72658-3_58 · Cited by 4
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“20 Nowadays, researchers have simulated the bioelectromagnetic fields generated by the brain, 21 heart, 22,23 and gastrointestinal tract 24,25 using current di-poles as volume sources.”
Durand, D., & Lin, J.-C. (1997) · IEEE Transactions on Biomedical Engineering · doi:10.1109/10.552247 · Cited by 3
“Moreover, the source currents have been limited to current dipoles [1], [7]–[10].”
BackgroundInfluentialMiller, W. T. I., & Geselowitz, D. (1974) · Annals of Biomedical Engineering · doi:10.1007/bf02368094 · Cited by 3
Self-citationNeuromagnetic Inverse Solutions in Terms of Multipoles
Haberkorn, W., & Burghoff, M. (2001) · doi:10.1515/bmte.2001.46.s2.100 · Cited by 3
“Note that for vanishing source extent these moments reduce to the magnetic multipole moments of a single current dipole [6], The location of the geometrical center and the electric dipole moment of the line current can be determined from the magnetic multipole moments 0,, and j32l presented in Eq.”
BackgroundOkada, Y., & Xu, C.-B. (1994) · doi:10.1007/978-1-4899-1307-4_28 · Cited by 3
Data-driven analysis for multimodal neuroimaging
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An algorithm to determine a dipole current in a sphere
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Parallel optimization applied to magnetoencephalography
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“To be more precise, from the quasi-static approximation [5], theseJp andB are governed by the Geselowitz equation [2,3], and if the shape of the brain is approximated to be spherical, then this equation is reduced to a simpler form[4] due to the simplification of the volume current term − ∇V , which arises in accordan…”
MethodElectric and Magnetic Fields of the Brain
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The relevant degrees of freedom of a focal source in MEG measurements
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Sensitivity of MEG and EEG to source orientation
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“Theoretically, a radially oriented current dipole produces no magnetic field outside a spherically symmetric volume conductor (Baule and McFee 1965; Grynszpan and Geselowitz 1973).”
BackgroundStudy on the low frequency magnetic detection sensitivity of cavity optomechanical magnetometer
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Principles and applications of simulations in the interpretation of ECG and EEG
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“Typical examples are a current dipole source in a homogeneous sphere, in a semi-infinite volume conductor (with a plane boundary), or in an infinite slab [10,11]. where cf>Sk is the electric potential at the kth surface, where the conductivity changes from a% to a~ (from inside to outside).”
Effect of torso geometry on the magnetocardiogram.
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Electric and Magnetic Fields of the Brain
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“Furthermore, a configuration consisting of a radial primary current and the associated volume current does not produce any magnetic field outside of a spherically symmetric conductor [8, 11, 12].”
BackgroundCurrent dipole estimation from magnetospinogram with 3-D planar sensor array
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“Modern SQUID-gradiometers and magnetometers permit to register weak magnetic fields, which are created by human heart, brain, muscles, see ‘Burstein & Cohen (1985, pp. 2640-2646)’, ‘Grynszpan & Geselowitz (1973)’, ‘Karp (1981, pp. 219-230)’, ‘Hämäläinen & Hari (1993, vol. 65)’, etc.”
BackgroundModel studies of spreading electrical activities in the brain on MEG/EEG inverse problem
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“a o th MC do not yet a t t "Do th contain inform t contained in the ECG? tz(8) .”
Background
Metadata
- 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)
- 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
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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