Simultaneous analysis of the cardiac electric and magnetic fields using the scalar multipole expansion

Titomir, L. I.; Kneppo, Peter

doi:10.1007/bf02459649

Cited by 6 publications

(5 citation statements)

References 15 publications

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“…One of the most recent works in this area was reported by Haueisen et al, who found different patterns of the mapping of MCG and ECG produced by artificial open loop current in a body phantom [3]. In other words, MCG surely provides some differentiating information about the electrical activity besides the ECG.According to the Helmholtz theory, the equivalent source of electrical activ ity, either electrical potential or current, consists of a flow (rectilinear) component and a vortex (close-loop) component [4]. ECG can only provide the information about the flow part of the electrical potential source.…”

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confidence: 80%

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Modeling of cardiac electrical activity for characterizing vortex components

Lin

Jiang

2011

2011 IEEE International Symposium on IT in Medicine and Education

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In this study, source model for solving biomagnetic inverse problem is developed with a new method, where vortex components along with the flow component of the equivalent source is considered. The model is an aggregation of a single current dipole and a magnetic dipole. The single current dipole denotes the flow component while the magnetic dipole is an abstract of the vortex component of the biomagnetic source.Simulation results indicate that this model could be more efficient for modeling cardiac electrical activity, compared with single current dipole. Despite that this model is more complicated than the single current dipole model; simple algorithm can still be used for solving inverse problem with only small revision. Meaning of the model parameters solved from the inverse problem is also discussed.Keywords-Modeling; Magnetocardiography; vortex source; magnetic dipole; current dipole I.INT RODUCTION Magnetocardiography (MCG) and Electrocardiography (ECG) are both non-invasive biomedical functional imaging method for cardiac electrical activ ity. However, the problem is whether these two approaches could provide complementary information for each other.Some theoretical and experimental efforts have been made to verify that MCG could provide more valuable information besides ECG. In 1982, Wikswo et al. suggested that a kind of electrically silent magnetic field could be detected by magnetic detection device [1]. Brockmeier et al. proved this theory by experiments [2]. They found that when the subjects were stress induced, there were dramatic changes in the MCG while no comparable changes in the mu lti-lead ECG. One of the most recent works in this area was reported by Haueisen et al, who found different patterns of the mapping of MCG and ECG produced by artificial open loop current in a body phantom [3]. In other words, MCG surely provides some differentiating information about the electrical activity besides the ECG.According to the Helmholtz theory, the equivalent source of electrical activ ity, either electrical potential or current, consists of a flow (rectilinear) component and a vortex (close-loop) component [4]. ECG can only provide the information about the flow part of the electrical potential source. But MCG can detect the magnetic field produced by both vortex and flow part of the current source [2]. This brings the difference between mappings of MCG and ECG. So models of the cardiac current source in MCG study should include the vortex co mponent of the source.In this study such a model for the equivalent source of cardiac electrical activity is proposed. In section the mathematical fundament of our model is presented. Higherorder terms in mu ltipole expansion is o mitted to obtain this new equivalent model. It can be formatted as an aggregation of a single current dipole and a magnetic dipole (Equivalent Current and Magnetic Dipole, ECMD). In section , we simulate the characteristics of the field produced by our model and compare this model with an equivalent single current dipole model. In secti...

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mentioning

confidence: 80%

“…According to the Helmholtz theory, the equivalent source of electrical activ ity, either electrical potential or current, consists of a flow (rectilinear) component and a vortex (close-loop) component [4]. ECG can only provide the information about the flow part of the electrical potential source.…”

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confidence: 99%

Modeling of cardiac electrical activity for characterizing vortex components

Lin

Jiang

2011

2011 IEEE International Symposium on IT in Medicine and Education

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“…The magnetic field of a localized impressed current source has been studied [35] by decomposing the total field into an irrotational component B (2) and a component B (1) that results from the radial electric quadrupole so that

B = {boldB}^{(1)} + {boldB}^{(2)} .

In the reference frame where a 21 , b 21 and b 22 are zero, the magnetic field is

{boldB}^{(1)} = \frac{1}{3} B (a_{20}) + 2 B (a_{22}^{3}) .

The irrotational component B (2) can be expressed as the gradient of a magnetic potential V m , which in turn is represented by a spherical harmonic expansion

Φ_{m} = \frac{1}{4 π} Σ_{n = 3}^{\infty} Σ_{m = 0}^{\infty} \frac{P_{n}^{m}}{r^{n + 1}} [A_{n m}^{M} \cos (m θ) + B_{n m}^{M} \sin (m θ)]

Expressions for the magnetic moments are derived [35] by utilizing the condition that the radial component of B (2) is also the radial component of B . There is only one non-zero magnetic dipole moment for each of the electric dipole representations of the electric quadrupoles.…”

Section: Magnetic Field Calculationmentioning

confidence: 99%

“…It is the radially directed current dipoles with no radial magnetic field and no magnetic dipole moment from which Titomir and Kneppo [35] constructed B . Furthermore, the other two representations for each quadrupole have the same non-zero magnetic dipole moment with equal magnitude but opposite signs.…”

Section: Determination Of the Current Dipole Configurationmentioning

confidence: 99%

“…In magnetogastrography, multipole models are important for the characterization of abnormal electrical activation patterns in the stomach due to gastroparesis and ischemia [15]. Several authors have addressed the information that is obtainable by inferring current dipole distributions from measurements of electric potential as opposed to measurement of the magnetic field of the heart or brain [18, 19, 35-37]. Two key advantages of multipolar modeling over dipolar models are that (1) multipole coefficients can be uniquely determined if they are used to model those source components that produce a non-vanishing field outside the volume conductor and (2) the multipolar approximation is mathematically close to the approximation of a few dipoles, but with the added benefit that the former can better describe extended sources [31].…”

Section: Introductionmentioning

confidence: 99%

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

2009

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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.

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Multipole Approach to the Inverse Problem in Electrocardiology: Convergence of the Multipole Equivalent Generator on the Inhomogeneous Body Conductor

Muynck

Cornelis

Titomir

2000

Bulletin of Mathematical Biology

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The multipole approach to the inverse electrocardiological problem consists of estimating the multipole components of the cardiac electric generator, starting from the measured body surface potential. This paper presents a critical investigation of the basic premise for the applicability of the multipole approach, namely the convergence of the multipole equivalent generator for the heart on the surface of an inhomogeneous body conductor. As an extension to multipole theory, a criterion for the convergence is derived. Based on realistic models for the body conductor and the cardiac electric generator, we observe that the criterion is not strictly satisfied in realistic conditions. Numerical simulations with the same models point out that the multipole equivalent generator is indeed not convergent in the strict mathematical sense. On the other hand, we show that the multipole equivalent generator yields a rather close approximation of the electrocardiological potential for intermediate values of the order of the multipole generator. A discussion is given on how to explain the apparently ambiguous results for the estimation of cardiac multipole components.

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Simultaneous analysis of the cardiac electric and magnetic fields using the scalar multipole expansion

Cited by 6 publications

References 15 publications

Modeling of cardiac electrical activity for characterizing vortex components

Modeling of cardiac electrical activity for characterizing vortex components

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

Multipole Approach to the Inverse Problem in Electrocardiology: Convergence of the Multipole Equivalent Generator on the Inhomogeneous Body Conductor

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