Electroencephalographic Source Reconstruction by the Finite-Element Approximation of the Elliptic Cauchy Problem

Malovichko, Mikhail; Koshev, Nikolay; Yavich, N.; Razorenova, A.M.; Fedorov, Maxim V.

doi:10.1109/tbme.2020.3021359

Cited by 6 publications

(2 citation statements)

References 48 publications

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“…A big number of comparatively effective methods were developed in the neuroimaging area. Recently, several promising approaches based on the solution of the ill-posed Cauchy problems for elliptic PDEs were proposed by various mathematicians [7, 10, 12, 13, 28, 33, 36], including some ML/AI-based methods [41]. One of the further works in the nearest future will be devoted to development of high-accuracy algorithms for reconstruction of the mass MNPs distribution and validation of it in the real MPI/MRX experiments.…”

Section: Discussionmentioning

confidence: 99%

Yttrium-iron garnet film magnetometer for magnetic microparticles in vivo registration studies

Koshev

Kapralov

Evstigneeva

et al. 2022

Preprint

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In the current article, we present a new kind of magnetometer for quantitative determination of magnetic objects in biological fluids and tissues. The sensor is based on yttrium-iron garnet film with optical signal registration system. Inheriting the working principle of a fluxgate magnetometers, the sensor works at a room-temperature, its wide dynamic range allows the measurements in an unshielded environment. A small size of sensitive element combined with a short recovery time after the excitation coils are off provide us with a potentially high spatial and temporal resolution of measurements. We show the feasibility of the sensor by sensing the remanent magnetization of Magnetic Nanoparticles (MNPs) both in vitro (test tubes, dry MNPs) and in vivo (local injection of the MNPs into mice).

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Section: Discussionmentioning

confidence: 99%

Yttrium-iron garnet film magnetometer for magnetic microparticles in vivo registration studies

Koshev

Kapralov

Evstigneeva

et al. 2022

Preprint

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“…It involves finding a solution to the Poisson equation inside a domain, given values on a subset of the boundary. Various numerical methods have been developed to tackle this problem, such as the boundary element method [33,34,[40][41][42], finite element method [18,34,[43][44][45], and finite difference method [28,46]. These methods typically rely on mesh-based discretization techniques and have proven to be effective in solving the linear Cauchy problem.…”

Section: Introductionmentioning

confidence: 99%

Polynomial Approximation of a Nonlinear Inverse Cauchy Problem

2023

acad. sci. j.

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In this paper, a class of nonlinear inverse boundary problem in the context of heat transfer is considered. We consider a class of nonlinear inverse boundary problems in the context of heat transfer. The problem involves determining the temperature distribution within a domain subject to a Cauchy boundary condition on a part of its boundary. We introduce a transformed variable, which allows us to reformulate the problem as a linear Cauchy problem followed by a series of nonlinear equations. We propose a polynomial expansion method to solve the linear Cauchy problem for the Laplace equation, and we employ the Newton method to solve the resulting nonlinear equations. Importantly, our approach does not rely on mesh-based discretization, allowing for parallel computation and preserving the mesh-free nature of the problem. We present numerical results obtained using our methodology and discuss the effectiveness of the proposed approach. The results show that the method provides a robust and efficient framework for solving nonlinear inverse boundary problems in heat transfer, with potential applications in various engineering and scientific fields.

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Meshless Methods to Noninvasively Calculate Neurocortical Potentials from Potentials Measured at the Scalp Surface

Nachaoui

Tadumadze

2023

Springer Proceedings in Mathematics &Amp; Statistics

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Electroencephalographic Source Reconstruction by the Finite-Element Approximation of the Elliptic Cauchy Problem

Cited by 6 publications

References 48 publications

Yttrium-iron garnet film magnetometer for magnetic microparticles in vivo registration studies

Yttrium-iron garnet film magnetometer for magnetic microparticles in vivo registration studies

Polynomial Approximation of a Nonlinear Inverse Cauchy Problem

Meshless Methods to Noninvasively Calculate Neurocortical Potentials from Potentials Measured at the Scalp Surface

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