ULF/ELF electromagnetic fields produced in a conducting medium of infinite extent by a linear current source of finite length

The paper reviews certain integral equation approaches and related numerical methods used in studies of biomedical applications of electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is analyzed by solving the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is carried out via Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current source, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-differential equation solved by means of the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, are presented in the paper.

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Integral Equation Formulations and Related Numerical Solution Methods in Some Biomedical Applications of Electromagnetic Fields

International Journal of E-Health and Medical Communications ◽

10.4018/ijehmc.2018010105 ◽

2018 ◽

Vol 9 (1) ◽

pp. 65-84 ◽

Cited By ~ 3

Author(s):

Dragan Poljak ◽

Mario Cvetković ◽

Vicko Dorić ◽

Ivana Zulim ◽

Zoran Đogaš ◽

...

Keyword(s):

Integral Equation ◽

Numerical Solution ◽

Nerve Fiber ◽

Electromagnetic Fields ◽

Biomedical Applications ◽

Current Source ◽

Wire Antenna ◽

Myelinated Nerve Fiber ◽

Myelinated Nerve ◽

Numerical Solution Methods

The paper reviews certain integral equation approaches and related numerical methods used in studies of biomedical applications of electromagnetic fields pertaining to transcranial magnetic stimulation (TMS) and nerve fiber stimulation. TMS is analyzed by solving the set of coupled surface integral equations (SIEs), while the numerical solution of governing equations is carried out via Method of Moments (MoM) scheme. A myelinated nerve fiber, stimulated by a current source, is represented by a straight thin wire antenna. The model is based on the corresponding homogeneous Pocklington integro-differential equation solved by means of the Galerkin Bubnov Indirect Boundary Element Method (GB-IBEM). Some illustrative numerical results for the TMS induced fields and intracellular current distribution along the myelinated nerve fiber (active and passive), respectively, are presented in the paper.

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Electromagnetic fields of a Röntgen current source

Journal of Physics B Atomic Molecular and Optical Physics ◽

10.1088/0953-4075/39/15/s18 ◽

2006 ◽

Vol 39 (15) ◽

pp. S725-S731 ◽

Cited By ~ 2

Author(s):

T Thirunamachandran

Keyword(s):

Electromagnetic Fields ◽

Current Source

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Electromagnetic induction by a finite electric dipole source over a 2-D earth

Geophysics ◽

10.1190/1.1443406 ◽

1993 ◽

Vol 58 (2) ◽

pp. 198-214 ◽

Cited By ~ 75

Author(s):

Martyn J. Unsworth ◽

Bryan J. Travis ◽

Alan D. Chave

Keyword(s):

Finite Element ◽

Electromagnetic Fields ◽

Electric Dipole ◽

Numerical Solutions ◽

Current Source ◽

Three Dimensional ◽

Iterative Solution ◽

Electromagnetic Response ◽

Dipole Source ◽

Horizontal Electric Dipole

A numerical solution for the frequency domain electromagnetic response of a two‐dimensional (2-D) conductivity structure to excitation by a three‐dimensional (3-D) current source has been developed. The fields are Fourier transformed in the invariant conductivity direction and then expressed in a variational form. At each of a set of discrete spatial wavenumbers a finite‐element method is used to obtain a solution for the secondary electromagnetic fields. The finite element uses exponential elements to efficiently model the fields in the far‐field. In combination with an iterative solution for the along‐strike electromagnetic fields, this produces a considerable reduction in computation costs. The numerical solutions for a horizontal electric dipole are computed and shown to agree with closed form expressions and to converge with respect to the parameterization. Finally some simple examples of the electromagnetic fields produced by horizontal electric dipole sources at both the seafloor and air‐earth interface are presented to illustrate the usefulness of the code.

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