Integral equation models in some biomedical applications of electromagnetic fields: Transcranial magnetic stimulation (TMS), nerve fiber stimulation

Poljak, Dragan; Cvetković, Dragoš; Dorić, Vicko; Zulim, Ivana; Đogaš, Zoran; Vidaković, Maja Rogić; Haueisen, Jens; Drissi, Khalil El Khamlichi

doi:10.1109/splitech.2016.7555936

Cited by 4 publications

(1 citation statement)

References 17 publications

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“…Also, in ordinary and partial differential equations we can convert several initial and boundary value problems to an equivalent integral equations. In recent years fractional differential and integral models act an essential role in describing various processes in many real-life situations in different fields such as mechanics, mathematical biology, economics, medicine, and many others (see [2,5,11,12,16,18,21]). As a contribution to the non-fractional approach, El-Sayed et al studied in [11] the sufficient conditions which guarantee existence, uniqueness, and continuous dependence of solution for a Cauchy problem of a functional differential equation of self-reference (ψ(t) = t), and state-dependence (ψ(t) t) on the form one continuous solution.…”

Section: Introductionmentioning

confidence: 99%

Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function

Youssef¹

2020

J. Nonlinear Sci. Appl.

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In the present article, we study the solvability of a class of fractional functional integro-differential equations of the Caputo-Katugampola type. The existence of solutions is investigated under sufficient conditions as well as the assumptions which guarantee the uniqueness of the solution is explained. Also, we examine the continuous dependence of the solution on the initial condition, the lag function 0 ψ(t) t, and the considered nonlinear functional. We give an example to explain our results. The outcomes in this paper extend the results developed by El-Sayed et al. in [A.

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Section: Introductionmentioning

confidence: 99%

Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function

Youssef¹

2020

J. Nonlinear Sci. Appl.

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Biomedical Applications of Electromagnetic Fields

2018

Computational Method in Electromagnetic Compatibility

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

Poljak

Cvetković

Dorić

et al. 2020

Data Analytics in Medicine

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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 models in some biomedical applications of electromagnetic fields: Transcranial magnetic stimulation (TMS), nerve fiber stimulation

Cited by 4 publications

References 17 publications

Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function

Caputo-Katugampola fractional Volterra functional differential equations with a vanishing lag function

Biomedical Applications of Electromagnetic Fields

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

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